The Activity Feed is shown on the first tab of a child's profile:
It displays the child holiday days and sick days as well as photos that their parents have tagged them in from News Feed posts.
You can add a new activity from the child's profile simply by clicking on 'Add':
To determine what's available, you can see which updates you have selected for a room in the Settings under 'enable tracking for':
You can of course also add custom statuses from Setup > Rooms > Statuses. See more here.
These types of updates are most commonly added from the Overview of the room, once clicking on a child's icon > Status:
When logging an update from the overview, you can expect it to land on the child's Activity Feed too!