(This started out as a comment on a friend's blog post, but it got too long, so rather than use up space on their blog, I thought I'd post my reply here instead)
A friend of mine wrote a reply to an article attempting to explain the purpose of internet memes (You might want to read those posts, or at least my friend's post). I'm sure everyone and their grandmother has a theory as to why memes exist. Now, I may not be old enough to be a grandmother, but I do have my own theories.
I think memes serve the same purpose as inside jokes, small-talk, and circumcision -- to say "Hey, I'm part of the same group you're part of!" It's like a social codeword to say "You can trust me, I'm one of you". I don't think they're fundamentally different from inside jokes, which have existed for all of human history, except that memes have the advantage of digital technology and speed.
As with any codeword, the more information it contains, the better. Obviously, a picture contains more information than a word. Not so obviously, taking an orthographically correct sentence and putting specific errors into it also gives it more information (e.g. "I can has cheezburger?" contains more information than "May I have a cheeseburger?"). If medieval stonemasons could have carried around pictures of cheeseburger-loving cats as a sign of gregariousness, they would have done so.
And yeah, this gives a context to what you're about to read. I don't agree that there has to be a visual stimulus for this context. Just writing the phrase "Y U NO," "Seems legit" or "The Game" brings up instant connotations to those familiar with them, same with hearing the first few seconds of "Never Gonna Give You Up". It's true that visual icons can pack in the most information with the least effort on the part of the viewer, but at our core, humans are closer to being semantic engines than visual engines.
I suppose you could argue that memes can serve as entertainment in themselves, and many of them start out that way, but they tend to just lose this entertainment value and become symbols in themselves. Maybe I'm alone in this, but I just don't find memes like "X all the Y" and "Y U NO" intrinsically funny. This isn't necessarily a bad thing, as long as they still function as social codewords.
Due to the speed of the internet, memes can spread quickly, but they can also become old quickly -- I was tired of "arrow in the knee" jokes before I had even heard one. As with other codewords, memes get switched around every so often. "All Your Base" seemed like it was going to last forever, but it's a little outdated nowadays, and I suspect that even memes as ubiquitous as the Rage faces and X all the Y will eventually go that way as well.
TL;DR version (another meme!): I think it's true that memes use context to pack a lot of information into a small space, but this is a part of their primary purpose as social "codewords".
Bonus - My Favourite Memes
PTSD Clarinet Boy
Horatio from CSI Miami
Cracked: 7 Memes That Went Viral Before The Internet Existed
The Original Article
My Friend's Reply
Know Your Meme