Snickerd00dle described it initially as:
what I thought I would do is pick ten games that I own and have never beat, that are regarded as classics by most people and are also games that I really wish I had played through, games everyone talks about that I never ended up finishing, and beat all ten of them by the end of the summer.
So that's the basic gist. Your own subjective definition of "Summer" (May-August, June-September, etc.) is fine...just mark an end date and shoot for it!
So what game are you ashamed to admit you've never beat? What titles have been sitting on your shelf for a long time that you know you should play? Put them on your list of 10! The goal is to give all of your picks - each of which should be regarded as at least a minor classic - the 'ol college try. You may find that you do indeed hate that "classic" with a passion, but at least now you'll have experience to back up that claim! The challenge gets even more enjoyable when multiple people play the same game, so consider adding to/modifying your list before you actually get started.
Here's my own tentative list, which may change as I see people add things to their own. I plan to get started in about a week.
1. Capcom vs SNK 2 EO
2. Super Metroid
3. Diablo II (played about 1/4)
4. Steel Battalion
5. Star Fox (played about 3/4)
6. Time Crisis (played about 2/3)
7. Sly Cooper (played about 1/4)
8. Panzer Dragoon Orta
9. Final Fantasy IV
10. Road and Track Presents: The Need for Speed (can't be "beaten" but I put enough time into to call it "done")
The games I have knocked off in previous summer challenges: