Ajax comes and goes pretty quickly, but he's the one man to whom Sula develops a true attachment. We first encounter him when Sula and Nel are young girls and he is twenty-one. He seems kind of creepy (he calls them "pig meat"), but he sparks something in Sula that stays with her until she's an adult. When she returns to the Bottom and they start sleeping together, we learn a little more about him. He has relationships with multiple women, whom he apparently treats well. And he's completely devoted to his mother. In fact, aside from his mother, he only cares about planes. (Maybe he sees them as a sort of escape.)
His relationship with Sula is easy and satisfying at first. But he senses that the sex between them is starting to mean something more to Sula, and this scares him off. On the one hand, he makes no promises to her of a committed relationship, and Sula seems content with this arrangement at first. But the fact that he is unwilling or unable to stick around when a woman starts to care about him raises questions about his character.
What are we supposed to make of the fact that nearly all of the males in the novel leave the women in their lives? Ajax is particularly interesting because he stirs something in Sula that she's never felt before. She doesn't fall in love with him, but she wants to "possess" him, and this is uncharted territory for her. Through Ajax we see a new side of Sula, and this makes him a unique male figure in the novel.