The red number on your activities icon corresponds with the number of activities that require your immediate attention.  Specifically, that number is the combined amount of overdue activities and activities that are due today.

Sometimes, the red counter in the Activities tab may show a smaller number than the List View of your Activities.
This is because the List View is filtered to show activities assigned to 'Everyone' in the company Pipedrive account. 

For reference, the List View of the Activities tab shows all the activities in the company that are visible to you.
If you'd like to see a list containing only your own activities, you can filter your activities and select your name under Owner. 
For a summary of all of the status of the activities, click the ? in the activity summary.