It's asynchronous pvp, when you play your cards and stats are recorded for each level. People who play after you have a chance to play against your build.
Auto-battlers are fairly popular games these days with lots of numbers flying all over the place. It’s the type of game that you have play a few times to really understand what’s going on. It already sounds like you are starting to get some of it. Yes, the bar at the bottom does indicate when the bees are about to come out, honey is gold (I thought it fit the theme of the bees). Everything is color coded as well, so all the healing cards are purple and purple numbers appear when you heal, green for poison, yellow for shields and so on. The boxes under the player names show how many wins they currently have against other players. Some of this is explained at the bottom of the game page, but if I go into too much detail for a game jam that will turn off people.
Thank you for playing.