We first met Tom in Mark Twain's previous book, The Adventures of Tom Sawyer.
Tom Sawyer is Huck's good friend, introduced in a previous book by Mark Twain, The Adventures of Tom Sawyer. And he is—well, he's basically like any pre-teen kid who spends his time reading adventure novels or too many comic books. He's imaginative, mischievous, and totally, hilariously, impractical.
Maybe Huck admires Tom because they're so different. Sure, Tom has a stable home and a good upbringing (a "character to lose" [33.21], as Huck puts it), but he's different from Huck in other ways. Where Tom is imaginative, Huck is practical. Where Tom always has his nose in a book, Huck runs away to the river or woods when he needs to escape. Where Tom is basically a good-hearted kid who's oblivious to moral issues, Huck is a boy on the verge of becoming a man by grappling with some really important questions.
And Huck definitely has a little bit of a man-crush on Tom. Huck wishes he could come up with a story as good as Tom's, or come up with a plan as good as Tom's. Why? Maybe because Huck seems that Tom has all the things he doesn't: "here was a boy that was respectable and well brung up; and had a character to lose; and folks at home that had characters; and he was bright and not leather-headed; and knowing and not ignorant; and not mean, but kind; and yet here he was, without any more pride, or rightness, or feeling, than to stoop to this business, and make himself a shame, and his family a shame, before everybody" (33.21).
So, respectability, a good upbringing, character, intelligence, kindness: we'll admit it, that's pretty impressive. But it's not everything. In the end, Tom lacks the most important thing: moral rightness.
Miss Watson can't see things clearly because her religion teaches her false principles (like, black people should be enslaved). Jim is hopeless, because his system of superstition is a complete fantasy. But Tom has his own fantastical system of rules leading him astray: literature.
He's always trying to do things the way they're done in books, like starting a "band of robbers" and making everyone write their names in blood (2.10). When Huck comes up with completely logical and honestly kind of easy ways to free Jim (like, lift up the bed and slip the chain off), Tom rolls his eyes: "Why, hain't you ever read any books at all?… Who ever heard of getting a prisoner loose in such an old-maidy way as that?" (35.6).
And it may be just a game to Tom, but remember: this whole time, Tom knows perfectly well that Jim is actually a free man. Tim is supposed to be the well-brought up kid with good principles and a solid conscience, but he lets Jim suffer for days, using him to act out some adventure fantasy he read in a book.
So, now who's the admirable one?