Unrequited love is a kind of love that can't be reciprocated or returned, even though it's usually desired. In the novel, one of the major characters, Jay Gatsby, has this sort of romance towards his old flame, Daisy Buchanan. When he went off to war, even though Daisy promised to wait for him, she couldn't and married Tom. Gatsby was poor and Daisy wanted more, desperate for affection. When Gatsby returned home, he did whatever he could to win Daisy's heart back and earned money and riches. Nick, Gatsby's neighbor, did the favor of reuniting him with Daisy but after all the time they spent together at his mansion, he still wanted more from her. He expected her to tell Tom that she has never loved him, and leave him, but she couldn't. She loved Tom and she'd be lying if she said she didn't. Daisy couldn't give the love that Gatsby expected from her.
Another example of an unrequited love in the text includes the relationship between Myrtle and Tom, which, in some ways, can relate to the one that Gatsby and Daisy share. Myrtle is married to poor man, George Wilson, and lives in the valley of ashes. She doesn't have much since they struggle with business, and yearns for more. She's not satisfied or content with what she has which brought her to a rich guy like Tom. With the kind of money that he has, he's able to provide her with the kind of "love" that she's been wanting and waiting for, but Daisy seems to get in the way between them. Even though Tom is cheating on Daisy, he still has much love for her, which holds him back from giving all of his love to Myrtle.
The love that Jay shares with Daisy and that Myrtle has with Tom is unrequited because the love is not returned, or at least, not enough love. Even though Daisy spends a lot of her time with Gatsby, he expects so much more from her, more than she can give because of her love for Tom. Myrtle is the same way around Tom, even though she has a husband of her own. Because of this unrequited love, Jay and Myrtle are overpowered by jealousy and selfishness.
sources: The Great Gatsby by F. Scott Fitzgerald