It's explained here: https://join-lemmy.org/docs/users/03-votes-and-ranking.html

Basically, Hot and Active show posts based on upvotes minus down votes, with a time decay so older posts rank lower.

Hot has the time decay based on created time, so you'll basically only see posts from the last day or so.

Active has the time decay based on the most recent comment, so if someone comments it can bring an old post back to the top.

There is also Scaled (if your instance has updated to 0.19), which is like Hot but posts from communities with less active users will get a boost so you don't miss out on posts in small communities from being drowned out by big community posts with lists of upvotes.