Crosbie is the dude whose murder gets everyone so interested in the giant web of strange occurrences and deceits that are going on in Hokitika. Since he's in the ground, he's associated with "Terra firma" in the novel's table of contents.
It looks super suspicious when a giant fortune is found in his cottage after his death (since he wasn't known to be wealthy in Hokitika), and then it looks even weirder when a wife no one ever knew about comes to claim it. However, it does turn out to be his gold…it just happened to make its way into his house in about the most circuitous and improbable way possible.
In fact, Crosbie wasn't ever expecting to see that money again, it seems. He had made a strike when he was mining the Otago fields, but his wife Lydia had stolen the yield and given it to her boyfriend, Frank Carver, so he could use the cash in a scheme to blackmail Alistair Lauderback (who, incidentally, was Crosbie's half-brother).
So, he had contented himself with carving a big C in Frank's face and skipping town. Little does he know the money is going to follow him (and so is Frank Carver) …but we'll get to that later.
We don't see a lot of Crosbie in the narrative, but we get enough to gain some sense of his personality and what makes him tick. First of all, we know that he writes his half-brother Alistair letters in the hopes of meeting him or their father (who fathered Crosbie out of wedlock to a prostitute). His letters are heartfelt and warm, and he seems genuinely hurt at times that Lauderback never wrote back. (Sadly, Lauderback was finally on his way to see Crosbie when Carver found and killed Wells.)
Despite the fact that he's a bit rough around the edges and perhaps crass, Crosbie seems to have a good heart. For example, when he's giving Anna the down-low on Lydia's conniving ways, he seems to take pleasure in scaring her with the revelation that the older woman's kindness is all an act:
'It's a line she spins. So you believe her, and you follow her home, and before you know it, you're beholden. Aren't you now? She's given you a fine meal and a hot bath and nothing but the milk of kindness, and what have you given her? Oh'—he wagged his finger—'but there will be something, Miss Anna Wetherell. There will be something that you can give.' (IV.5.49)
However, when he sees that his joking is upsetting Anna, he dials it back a little bit:
He seemed to perceive Anna's anxiety, for he added, in a gentler tone, 'Here's something you ought to know. There's no charity in a gold town. If it looks like charity, look again.' (IV.5.49)
So, even while he's giving Anna the straight scoop on how things work in Lydia's house of ill repute, he manages to check himself and avoid outright cruelty.
Although his letters to Lauderback read relatively well, his speaking style isn't super flowery or elegant. For example, when he's warning Anna about Lydia's plans to groom her for prostitution, he uses his typically plainspoken style:
It's quite all right. My old ma was a whore, God rest her. (V.1.12)
So, yeah, he's not the most refined speaker we have in the book.
Despite the fact that he likes to shock and alarm people from time to time, Crosbie really is a bit of a softie. When he found out that Anna had miscarried their baby, for example, he was fairly upset, and drank heavily with Emery Staines in his mourning. So, even as he was keeping up a tough front, you can tell here that he was definitely feeling something…and trying to drown it, apparently.