You know you have unread messages and unseen activity in a channel because its name appears bold. If you favorite the channel, it stays visible in your list.
You also receive notifications when someone @mentions you or replies to a conversation you're in, so that's another way you know a channel is active.
To keep up with what's happening in channels, tap Teams and select a channel. Tap Follow channel in the header. You'll get all the latest news in your activity feed from the channels you are following.