On Mastodon, you can customise your notifications to adjust what they tell you about and how they tell you.
On your server’s website, go to your Notifications column and click on the slider icon in the top right corner. This provides lots of options to customise, and there are even more options if you scroll the menu down a bit.
On the official app, go to the main timeline and click on the cog / gear icon ⚙️, then scroll down to the notifications section. The official app’s options are more limited though, you will see a lot more options on the website version.
Third party apps will have various different interfaces for customising notifications, but they’ll usually be in their settings section.