On the top right you will notice a little star icon, that is your favourites. It allows you to favourite certain items in Base, including listings, contacts and documents and easily access them from here.
When you open a contact or listing, simply click the favourite star icon to add it to your favourite list:
And in your library, click on the favourite icon next to a file to favourite it:
Favourites are saved on your account, so you'll be able to see them from any device.
Favourites are not shared with the office, so remains in your personal view.