Stamina gives your Hero the power to battle. Without enough Stamina, you can not enter the battle. The higher the Quest Node, the more Stamina your Heroes need to enter.
Luckily, Stamina recovers over time:
1 Stamina recovers every 5 minutes
1 Stamina can be instantly recovered for 2 GUM
If you decide to recover with GUM, a little message will show up and ask you to confirm before you spend your GUM.