My next-door neighbor had one of the little tamagotchi-like Neopets toys-- the ones with the clamshell designs and the little figurines, you know? He had a Kougra one, and I thought it was super neat, so I went and did some research before getting into the site.
I think the most appealing thing to me, as a dweeby little kid who made a fake birthday for 13+ priviledges, was the ability to form entire characters and stories around your pets. I was really, really into the petpage and roleplay scene, made friends who did art and beauty contest stuff, and those sorts of shenanigans.
I can still list off multiple really "famous"-ish pets by hand, it's a little silly. That's how ingrained I was in the culture.
I don't really do that stuff on Neopets as much as I used to-- I've moved to Subeta for my "virtual petsite as a story+character medium" fix, since it's a way more productive and less restrictive environment for that sort of creativity. But those old days on Neo still hold a fond memory in my heart, and I enjoy just kind of messing around, making and zapping and fostering pets nowadays.
I think I was about 9-10 when I first discovered Neopets with my best friend. Not sure what kept me attached, I've always liked games from a young age. However I think I became addicted because there was so much to do, so much account progress to be made. And I tend to sway more towards communities/games that allow you to make progress/choose your own sort of destiny.