From IndieWeb

clap is a feature introduced by Medium as a replacement for like and Medium's previous "Recommend" button. A user can clap multiple times to show how much they loved a post.

From the Medium blog post:

Rolling out to Medium users over the coming week will be a new, more satisfying way for readers to give feedback to writers. We call it โ€œClaps.โ€ Itโ€™s no longer simply whether you like, or donโ€™t like, something. Now you can give variable levels of applause to a story. Maybe clap once, or maybe 10 or 20 times. Youโ€™re in control and can clap to your heartโ€™s desire.

Medium plans to use the number of claps to determine how much to pay writers on their platform.

See also