In your Mighty Network, you have opportunity to follow other members. When you choose to follow another member, this will trigger more of that person's activity to show up in your feed. You will also get notified whenever that person posts something new.
To follow someone, just navigate to their profile and tap the button that says "Follow." That's it!
If you ever want to adjust your notifications for members you follow, go to your Profile Photo > Your Settings > Notifications. From there, you can toggle on or off the option to be notified whenever people you follow add new posts.