You can hand out as many bardic inspo dice as your cha mod and you regain them on long rest. (From level 5 on, you regain them on long or short rest.)

The die size starts as d6 and becomes a d8 at 5th level, a d10 at 10th level, and a d12 at 15th level.

As a bonus action, you can inspire someone else [do this diegetically] and give them a die.

Bard colleges also can do special things with these. In our party we have a lore bard and a sword bard.

Lore bards can do Cutting Words; giving their bardic inspo dice out as negatives; this costs reaction. A good way to save yourself or a pal from an incoming attack.

Sword bards can do Blade Flourishes; this doesn't cost action but can only be done when they hit with an attack.

Using dice you've been given by ANOTHER bard: this doesn't cost action but can only be done when you've just rolled an attack roll, an ability check (this includes tool proficiency checks as well), or a saving throw.