You can write about a time when you worked really hard to achieve something and then you got it, or even if you didn't get it, you still felt really good because you put in all that work. Or, you can talk about something that you kept pleading with your parents to buy for you and then they eventually caved in to your persuasion and perseverance and bought it for you. You can also include stories of famous people who didn't get what they wanted first but after a lot of hard work, it paid off and now they are famous for it, etc.
Asagai's main function as a character seems to be to inject the play with symbolism. Basically, Asagi is Africa. He represents one extreme of the American debate on assimilation. His presence in the play forces the audience (and Beneatha) to ask what it truly means to be an African American.