I took a brief look at the code for this recently.

Hot is similar to the old reddit ranking. A combination of upvote score with a decay over time, starting from when the post was made.

Active is essentially the same ranking, but the fade away is based on the time of the most recent comment on the post. Any new comment will bump it back up, resetting the timer. There is a 48 hour cut off, so posts don’t keep getting bumped up indefinitely.

From the Docs link available at the bottom right of any lemmy page, in “4. Votes and Ranking” :

• Active (default): Calculates a rank based on the score and time of the latest comment, with decay over time
• Hot: Like active, but uses time when the post was published