Depends a lot on the site’s overall vibe too..
Generally speaking, I’d say it can mean one of three things: (A) Really interested in making friends if that should occur, and/or (B) Open to “friends-with-benefits” (an ongoing relationship involving sex and friendship, but not romance/partnership, and maybe not “dating” in the sense of going out a lot together, etc.), and/or (C ) Looking for hookups/one-nighters, but the site either doesn’t have an option for “Intimate Encounter” or some such, or the person is reluctant to admit they’re willing to consider that, so they say “Friends” instead. ‘Course, if they’re thinking A, and you assume maybe they mean C, you’re likely to irritate them… ;-)
On sites that are almost entirely social networking (like Facebook), most people who say they want Friends probably mean A; relatively few mean B or C. On a site that’s not specifically about dating/matchmaking, but which a lot of people use that way anyway (like Tagged), then there’s probably a big mix of meanings. Same with sites dedicated to dating/matchmaking.
On sites dedicated to finding hookups (like Fling), it’s probably most likely to mean (D) People I’d be willing to chat with online, but not meet in real life. Because most folks are unlikely to use such sites specifically to find plain old buddies like in A, and they don’t need the double-meanings of B and C, because the site has clearer options for describing what they want…
On more or less all types of sites, I’d say that saying they want Dating means they want to go out on dates, but don’t want to specifically seek out a serious relationship yet. (Not necessarily that they’d turn it away if they happened to date the right person, but they’re not actively looking for it…)