Mastodon has two similar but significantly different features: Favourites and Bookmarks.
⭐ Favourites are the Mastodon equivalent of Likes, used to show appreciation. Click on the star below a post to favourite it. The author of the post is notified when you favourite it.
🔖 Bookmarks are for when you want to save a post and go back to it later. Click on the bookmark icon below a post (or in the ⋯ menu). Bookmarks are totally private, no one is notified.