You can follow companies so that you can track their progress without actually buying them. This allows you to see what price they were at when you first started following them against their current price.
To add a company to your watchlist, navigate to the company card that you're interested in following. You will see an outline of a yellow star in the top right hand corner. The outline means you're not currently following it.
Tap on the star and it will fill in yellow to indicate that you are now following this company and it will appear on your watchlist. Tapping again will unfollow and it will be removed from your watchlist.