Merton Densher is an attractive and charming young man who's in love with Kate Croy. The problem is that Kate's rich aunt and benefactress, Maud Lowder, doesn't approve of him because he's poor and low-class. On top of that, the snobbish aunt has a problem with Merton's Englishness.
Merton, you see, has spent much of his life moving around, whether it's through
"his early years abroad, his migratory parents, his Swiss schools, [or] his German university" (18.104.22.168). This theme of constant movement gives Merton's character a sense of never being quite at home. On top of that, his non-English education makes him even less respectable in Aunt Maud's eyes, because Aunt Maud is a firm believer in the superiority of English culture.
For all that, Merton has a way of making Aunt Maud like him quite a bit—just not as a potential in-law. Through his dealings with Kate, we can see that Merton is very diplomatic and, quite frankly, a bit of a pushover. As he says to Kate of their relationship, "You keep the key of the cupboard, and I foresee that when we're married you'll dole me out my sugar by lumps" (22.214.171.124). This is his way of saying that he plans on doing whatever Kate tells him to do, and he plans on liking it.
Part of this might come from the realization that, as a man with no money, his only hope is to make people like his personality as much as possible. This doesn't make him cynical or conniving, though. If anything, Merton Densher is one of the most moral people in this book.
Merton is such a nice, honest dude that it takes him nearly the entire book to figure out the plan that Kate is manipulating him into. At one point, Kate even becomes exhausted by "the amount of light men did need!—Kate could have been eloquent at this moment about that" (126.96.36.199). In other words, she's amazed at how much she has to spell things out for him—namely, that she wants him to propose to Milly so that he can inherit her money when she dies. Merton, though, is too honest and moral a man to understand what's going on. For his part, he thinks he's supposed to be nice to Milly because she's dying and it's the right thing to do.
As the book reaches its later stages, Merton starts to discover his independence. The more he feels like Kate's pawn, the angrier he gets. He shows this newfound independence by telling Kate why he would never lie to Milly about his and Kate's relationship, saying, "If I had denied you moreover […] I would have stuck to it" (188.8.131.52). In other words, if he'd followed Kate's orders and told Milly that he and Kate would never be together, he would have actually dumped Kate just to make sure he didn't make himself a liar. This is a pretty hardcore moral stance, since everything Merton has done in this book has been for the sake of marrying Kate. But unlike Kate's cynical approach, Merton is determined to do things only in a moral way that doesn't hurt anyone. Next to Milly Theale, the dude is basically the moral compass of the book.