The speaker is contemplating the best way of achieving happiness. He has decided that there is really only one thing—and one thing alone—which has the power to bring genuine happiness to a person. That one thing is the ability to look back at the end of the day with an honest and faithful assertion that that day belonged fully to him.
Owning the day means finding the joy within it regardless of the state of the weather. Owning the day means finding and owning the joy of the day regardless of the trials of fate, which are outside his control.
Happiness belongs to anyone who has taken control of his life in the present, and can therefore honestly tell fate to do their worst tomorrow since, on this day, he lived his life on his terms.
The poem ends with one final piece of advice. If, the speaker says, Heaven itself can't change the past, what use is there in worrying about it? One should accept the past, face the future, and most importantly, live in the present.