A Raspberry Pi is a computer about the size of a deck of cards that costs ~$40.
It's tiny, but it has decent specs.
1.2GHz 64-bit quad-core ARMv8 CPU, 1 GB RAM

All you need is a base OS installed, and then the emulators for whatever gaming console you want, and finally you need to save the game roms onto either the Pi or onto a flash drive that it reads.