Archibald Craven is the master of Misselthwaite Manor and Mary's guardian when her parents die, since he is Mary's uncle. Archibald is also the father of our other main character, Colin Craven. And while Archibald is not necessary a bad guy, he has caused a lot of trouble in his time with his deep neglect of Colin.
The thing is, Archibald hates to go home because he can't stand to look at Colin. He can't stand how much Colin looks likehis dead wife but does not act likeher in the slightest. And of course, Archibald's neglect makes Colin more and more spoiled and given to tantrums. It's a vicious cycle: By staying away, Archibald makes Colin less and less like his kind-hearted, beautiful Lilias. So Archibald is really making his own problems, here.
While we definitely don't approve of the way that Archibald treats his son, we can't deny that he passionately, and truly loved his wife. Even Mrs. Medlock (who isn't exactly a generous person) admits that the two of them were absolutely head-over-heels in love with each other. She tells Mary early on:
"He's got a crooked back […] He was a sour young man and got no good of all his money and big place till he was married." (2.46)
In other words, things were plenty rough for Archibald before he met Lilias, but she stepped in and changed his life without caring about the "crooked back" that seems to bother everyone else in the novel.
Once Lilias dies, it's as though Archibald has lost everything he cares about in the world. He believes at first that his son will die in a few days after Lilias's death, and then that Colin "would be a deformed and crippled creature" (27.29). Even when it becomes clear that Colin will survive, Archibald just can't deal with being a father in his state of deep depression.
As he goes on his round-the-world efforts to avoid his son, "darkness so brooded over him that the sight of him was a wrong done to other people because it was as if the he poisoned the air about him with gloom" (27.4). In other words, he's so miserable and unhappy that just looking at him hurts other people—something like the Sad Kanye meme, we guess.
The only thing that brings Archibald Craven back to Misselthwaite Manor—and to an understanding of his parental responsibilities—is a dream from his wife and a letter from Mrs. Sowerby telling him that he "would be glad to come home" (27.24).
While we're glad that Archibald finally cottons on to the fact that he has a ten-year-old son who needs him, we don't much like the fact that it takes a letter from a woman he's met once and a dream of a visitation from beyond the grave to remind him of that fact. Archibald's belief through most of Colin's life that his son is "a confirmed invalid, with a vicious, hysterical, half-insane temper" (27.29) should have been enough to convince him that Colin could use an extra helping hand from his own darned father.