Clara is Amory' Blaine's widowed distant cousin, and the only reason she pops up in Amory's life is because Monsignor Darcy sends Amory a note asking him to go see Clara. After all, the poor young woman has been left all alone with her children following her husband's death, and she needs someone to help cheer her up.
As the narrator tells us, "She had had a harried life from sixteen on, and her education had stopped sharply with her leisure" (1.4.212). In other words, Clara hasn't had much opportunity to learn the skills she needs to work and make money for her family. But despite her circumstances, she promises herself never to marry again because she wants to be with her children at all times.
When Monsignor Darcy asks Amory to visit Clara, he may or may not know that Amory is going to fall hopelessly in love with her. As we find out early on, Amory feels as though Clara is:
… the first fine woman he ever knew and one of the few good people who ever interested him. She made her goodness such an asset. (1.4.215)
Whoa, talk about kissing cousins.
But when we say that Amory is hopelessly in love, we really mean it. Clara has sworn off men for the rest of her life, and even though she likes Amory, her decision is final. Amory then has to retreat to his Princeton life and try to find something (or someone) else to help him find fulfillment.