"Maybe we've spent too long trying to figure all this out with theory... Love is the one thing we're capable of perceiving that transcends dimensions of time and space."
In this quote, Brand is arguing that her feelings for Wolf Edmunds, rather than skewing her judgment, are actually aiding it, and that love is a quantitative factor that should be considered along with their other data. Ironically, Cooper ends up agreeing with her. In the end, in the place that "they" (the aliens) created so Cooper could understand time as a place, it was Cooper's love for Murph that allowed him to cross time and space and communicate with her. In this way, Brand's quote foreshadows the film's climax.
Professor: "We must confront the reality that nothing in our solar system can help us."
Cooper: "Now you need to tell me what your plan is to save the world."
Professor: "We're not meant to save the world. We're meant to leave it, and this is the mission you were trained for."
Cooper: "I've got kids, professor."
Professor: "Then get out there and save them."
This quote, appearing after Cooper and Murph end up at the hidden facilities of NASA, shows what the priority of the government has become: to ensure that mankind survives, no matter the cost. In this scene, Cooper explains to the professor that he has children that he needs to get back to, but Professor Brand counters that their only hope for a future will be if he goes. This scene sets up the importance and the inevitability of the mission on which Cooper ultimately embarks. The stakes are as high as they could be possibly be, and for him to decline the offer becomes unthinkable.
"We've always defined ourselves by the ability to overcome the impossible. And we count these moments. These moments when we dare to aim higher, to break barriers, to reach for the stars, to make the unknown known. We count these moments as our proudest achievements. But we lost all that. Or perhaps we've just forgotten that we are still pioneers. And we've barely begun. And that our greatest accomplishments cannot be behind us, because our destiny lies above us."
In this quote, Cooper essentially summarizes both his rationale for why he has to go on his mission, and the ideals of humankind as a whole. He opens by noting that as a race, we have made some exceptional achievements, ones that people even half of a century ago would not have believed to be possible. He then explains that despite all that we have achieved, enough is not and never will be enough. The only achievements that we are proud of are those that we have not yet achieved. He says that humans must and will live on to witness these achievements.
"We used to look up at the sky and wonder at our place in the stars. Now, we just look down and worry about our place in the dirt."
Though Cooper is referring to humanity as a whole with this quote, it's particularly applicable to him, and indeed the "we"s in this sentence may well be replaces with "I"s. He explains that while space exploration was once something exciting, a chance to discover new things in the universe, in its efforts to ward of starvation, humanity has forgotten about the possibilities the universe used to hold. He laments his lost purpose as a NASA engineer and his new role as a "caretaker" for the Earth, and criticizes humanity's forgotten role as pioneers for whom the latest frontier was never enough.
"You might have to decide between seeing your children again and the future of the human race. I trust you'll be as objective then."
By this point in the film, it's been established that the odds of saving the human race through Plan A are getting slimmer. Cooper knows he has a duty to preserve humanity by whatever means necessary, even if that entails going with Plan B. Now he is faced with the harsh reality, as Brand explains to him in this quote, that if they're forced to do this, he will never see his children again. Brand is spitefully throwing this fact in his face as a response to his dismissal of her love for Edmunds when deciding which planet to head to next.
"When I was a kid, it seemed like they made something new every day. Some, gadget or idea, like every day was Christmas. But 6 billion people, just imagine that. And every last one of them trying to have it all. This world isn't so bad."
This quote is a direct commentary on present-day consumerism and over-population. Given that Interstellar takes place in the near future, Donald the old man is meant to represent those who were young in 2014 (the film's release year), those who knew a world of 6 billion people (and counting) and who vied for the next iPhone, the latest video game, or the newest car in a materialistic effort to improve their lives, all the while allowing the planet to suffer. His implication that the useless innovation and overpopulation of early-21st-century life make their dystopian world seem comparatively tolerable is a warning for the film's audience about the consequences of unchecked greed and hubris.
"Time is relative, okay? It can stretch and it can squeeze, but... it can't run backwards. Just can't. The only thing that can move across dimensions, like time, is gravity."
This moment foreshadows the film's climax in which Cooper uses gravity to communicate with Murph across time via the tesseract. Practically speaking, Cooper himself is unable to travel back in time to undo the tragic happenings on Miller's planet (as he wishes to do in the scene from which this quote comes), or any of the regrettable events that happen after, but Brand's acknowledgement that gravity could travel back in time sets the stage for when Cooper later becomes Murph's ghost, using gravity to knock the books off her shelf in the past, manipulate the dust to fall in lines on the floor, and ultimately transmit the quantum data from the black hole via the watch.
"After you kids came along, your mom, she said something to me I never quite understood. She said, 'Now, we're just here to be memories for our kids.' I think now I understand what she meant. Once you're a parent, you're the ghost of your children's future."
This quote by Cooper as he gives a tearful goodbye to Murph is particularly memorable not only for its poetic nature, but also for its ironic foreshadowing. The painful memories of Cooper and his traumatic goodbye will become all that Murph has left of him until the very end of her life, memories she uses to drive her pursuit of the answers to the gravity equation. By leaving on his mission, Cooper effectively makes himself the very thing his wife said he was: only a memory. And, of course, he will literally become the "ghost" in her bookshelf at the film's climax, so referring to himself as one in this instance is particularly ironic.
"Don't judge me, Cooper. You were never tested like I was. Few men have been."
As noted elsewhere in this guide, Dr. Mann becomes the great tragic character of Interstellar. While he was once touted as "the best of us," a brave soul who inspired others to sacrifice everything for the good of mankind, his long years of isolation on his unforgiving planet twist him in the other direction, into a man capable of displaying the worst of human behavior. He becomes not the bravest of the brave, but a coward, which he himself admits. Mann cites his torturous years alone as justification for this cowardice, and with this quote in particular he leaves open the question for audiences: is he to be judged and blamed for his malice, or is his behavior the tragic result of unbearable circumstances, something to which any human in a similar situation would have resorted?
"Brand. She's out there. Setting up camp. Alone, in a strange galaxy. Maybe right now, she's settling in for the long nap. By the light of our new sun. In our new home."
There is much to wrap up as the epic, nearly 3-hour Interstellar comes to a close. We know that (presumably most if not all of) humanity made it off of Earth in the space stations made possible by Murph's gravity breakthrough; we know that Cooper and TARS survived their journey into and out of Gargantua, and that Murph and Cooper end up with the closure they so desperately desired. But as for Brand, and the potential for a habitable new planet, only through this quote does Murph succinctly and dramatically wrap things up for us: Brand survived her slingshot ride around Gargantua and made it to Edmunds' very habitable planet. It orbits a star, unlike Miller and Mann's, and Brand is already establishing a settlement and waiting for others to arrive. With the shots of Edmunds' name plate and Cooper commandeering a Ranger, we additionally infer that Edmunds is dead and that Cooper is going to reunite with Brand to help her set up the new colony before the space stations arrive. As for what happens next for humanity, that extends beyond Interstellar's story, but for the purposes of wrapping up this complex film, this quote is intended to give the audience the closure they need to feel emotionally satisfied.