The die icon means you have to throw a d20 to do that said action.

Greeting

This action is something you can do once a day, you earn friend points & it adds to the clock.

Gather Intel

This action let's you ask a character if they've "heard any news" giving you the chance of maybe unlocking new areas or obtaining items.

Share A Moment

Based on your friendship with a character different paths will open up. having a good standing with a character could save their life. (sharing a moment will also gain you friend points)

You can only greet a character once a day and you have 3 dice rolls a day. Certain items or event might alter how the die roll work, such as luck bonuses or giving you extra throws.