"Run, Forrest, Run"
The overarching theme of the film is summarized in one of its most memorable lines of dialogue. A scene early in the film shows young Forrest getting bullied for his leg braces and intellectual limitations. His best friend Jenny urges him to run, in order to escape the bullies, even though they are on bikes and he is inhibited by his braces. Nonetheless, Forrest heeds her advice and begins to make a run for it, and as the intensity of his running increases, the braces break and fall off his legs. In this instant, Forrest feels empowered to run away from the issues that are hurting him, and is liberated by the promise of escape. Throughout the rest of the film, he uses running as a way out of various situations, a means of processing the overwhelming stresses of his life. When Jenny leaves him in the middle of the night, he runs across the country and becomes a national celebrity for his dogged determination.
The Wisdom of the Fool
A defining feature of Forrest Gump is his below-average intelligence. In the beginning of the film, he is deemed too dumb to even enter the public school system, but underneath his ignorance is a kind of wisdom. He sees the world though a literal perspective, barely able to understand abstraction or metaphor. This limits him in many ways, but it also allows him to cut through the hypocrisy and complication of the world to see the truth in situations. Forrest has an attachment to aphorisms and idioms that his mother taught him in order to get by, and sometimes they hold a lot of truth. Thus, the fool is shown to be wiser than many of the more sophisticated types around him.
History
In the beginning of the film, it seems as though Forrest's ignorance is bound to situate him on the outside of society, forever trying to gain access to a world that shuts him out. Ironically enough, quite the opposite comes to pass, and Forrest finds himself at the center of significant historical events. One of the main comic motors of the film is the fact that Forrest often finds himself at the forefront of historically significant events, including the integration of the University of Alabama, the All-American football team's visit to the Oval Office, and the Vietnam War. History is almost another character in the film, a backdrop for Forrest's various foibles.
Love
At one point, Forrest says to Jenny, "I may not be a smart man, but I know what love is." Love is a central theme in the film, and the relationships Forrest forges with the people he loves is an anchor for him throughout the ups and downs of life. His mother is a loving woman who teaches him to believe in himself, Jenny shows him love and acceptance when few others at school will, and both Bubba and Lieutenant Dan offer acceptance and care in pivotal moments in Forrest's life. Eventually, Forrest is united with the son he fathered with Jenny, and experiences the love that a father feels for a son. One of the last lines of the film is Forrest telling Forrest Jr. he loves him as he climbs onto the school bus.
Death
Forrest must face death several times in the film. First, he learns about death in the war, when his best friend Bubba dies, and he saves his fellow soldiers from the dangers of the war. Not long after, his mother dies of cancer, and on her death bed she tells him that "Death is part of life." His experience with death helps him understand the significance of life, but it also does not prepare him for the death of Jenny, his one true love. Forrest is saddened by Jenny's death and misses her fiercely, but he also takes the loss in stride, grieving it with the appropriate gravity while also sensing that she is still with him, even after her soul has left her body.
The Meaning of Life
At the end of the film, while visiting Jenny's grave, Forrest says, "I don't know if we each have a destiny or we're all just floatin' around accidental like on a breeze. Maybe both happening at the same time..." In this moment, he grapples with philosophical questions that seem like they should be beyond his realm of understanding. He meditates on the nature of life and death, and how to make meaning in a chaotic and unpredictable world. While his mother suggested that everyone has a destiny, that life and death are part of a meaningful tapestry that is somehow set up by a deity or entity, Forrest has his doubts about this. In the end, he suggests that destiny and chance are equally influential in how the world unfolds.
Purposefulness
What Forrest lacks in intellectual nuance he makes up for in singleminded-ness and a deep sense of purpose. He is good at football because it requires him to simply run and score a touch down, he is good in the army because it requires him to follow orders and complete very basic tasks, and he is good at becoming a shrimper because he is determined to honor Bubba's legacy, and keeps trying in spite of the obstacles. Forrest is defined by his sense of purpose and his unswerving loyalty and commitment to everything and everyone in his life.