I mean to reply to this ages ago but didn't! Better late than never, right?
So on Archive Of Our Own, a Kudo is basically like a thumbs up, every story says how many kudos it's received, you can sort by the number of "kudos", and the people who gave a kudos are listed at the bottom of each story. You can only give one kudos to a story.
As an author, the kudos are a nice little boost, on AO3 you can get notifications when you get kudos and that's fun. And, like high numbers of reviews and high star ratings, a higher number of kudos may draw my attention to a story. I remember you calling them "lazy reviews" and yes as an author I'd prefer written reviews but with kudos at lease I feel like I'm receiving some feedback and as a reader I can leave a little token for the author.
My trouble with the star ratings is that first it's not a universally agree-on scale. Some reviewer may be very stingy with 4 or 5-star ratings, while others give out 5-stars constantly. And if a story had 1 5-star rating or 20 5-star ratings, it appears the same in the archive listing. Kudos are pretty black-and-white, you either like the story enough to give a kudos or you don't, there's less room for misunderstanding.