You should use 15 amps when you're only powering things on the circuit like lights, fans, computers, TV or other low amp devices.
You should use 20 amp when you're powering things such as fridge, freezer, heaters, air conditioners and other high amp drawing devices.
15 amp wires, breakers and circuits are often used for lighting, fans and often seen running through the ceiling to power ceiling fans, bedroom lights, bathroom lights and other lighting fixtures.
However many people now wire all circuits including light circuits with 12 amps and use 12-2 wire.
15 amp wire is 14-2 and costs a bit less than 12-2 wire but wiring all circuits in 12-2 wire is just easier.
A 20 amp electrical circuit requires wiring and outlets rated for 20 amps.
If you run 20 amps of electricity over 14-22 wiring, which you would use for 15-amp circuits, you run the risk of the wire overheating and melting and causing an electrical fire.
Things and appliances that need a 20 amp outlet and 20 amp circuit include.
Refrigerators, blenders, microwave ovens, and other high-power kitchen appliances.
Drills, saws, air compressors, and other types of power tools and heavy equipment.