There are two sections: "Latest" and "Hot". If your meme is 'Submitted', it's in limbo until a Moderator decides to change it to 'Featured'. Among other things, they have to determine if your meme violates imgflip's TOS.
Once 'Featured', all memes go to "Latest" in the order that the Moderators change it's status from 'Submitted' to 'Featured'. If a lot of users are submitting memes at the same time, many pages worth of memes can appear at once, and yours could end up anywhere in the many, many, many pages of "Latest" memes, your clever humor and expert photoshopping forever lost in a seething crowd of angry political rhetoric, non-sequiturs, and astounding examples of unintelligible stupidity that is 70% of what gets submitted on this site.
"Hot" memes are listed in the order of those which have the most upvotes and/or comments. I think it's some combination of both, because I've seen memes on what locals call the "Front Page" (page 1 of 'Hot') with lots of comments and relatively few upvotes, and vice-versa. I cannot tell you which weighs more, comments or upvotes, or if they weigh the same.
Upvotes and comments are acquired through a combination of dumb luck (someone happens to bump into your meme, and in true needle-in-a-haystack fashion, also happens to think it's clever or comment-worthy), and being so notoriously famous for making good memes, that many people regularly visit your Profile page because they know they'll find funny stuff there.