Can a Nintendo 3DS battery be used to power a pcb?
You probably bought a boost converter or something similar, a boost converter takes a small input voltage in your case 3.7V and gives a larger output voltage in your case 5V. 

A boost converter achieves the higher output voltage by sacrificing current. It will draw much more current from the battery at 3.7V than it can deliver at 5V.

You must make sure the battery can deliver the required current. 

Trying to draw more current than the battery is rated for can damage the battery and with a lithium battery, damage can start a fire. 

A boost converter is a type of switched mode power supply and as with all switched mode supplies it will be very noisy - so make sure you filter it properly (there will probably be guidance in the datasheet).