A MIDI interface allows you to connect midi hardware (controllers and sound modules). Typically a MIDI interface connects to your computer via USB or FireWire and contains the 5-pin DIN MIDI connectors. This lets you connect a MIDI-enabled piano, beat pad, etc. to control music production software. The MIDI interface does no actual sound reproduction.
MIDI is NOT sound! MIDI is data capable of triggering equipped musical devices.
For instance, if you have a computer with music production software (ProTools, Logic, Cubase, GarageBand, etc.), a MIDI interface allows you to connect your cheap Casio keyboard and control sound generated by your computer... your cheap Casio could then potentially sound like a Rhodes electric piano, Steinweg grand, or Hammond organ--or dogs barking, drums from space, etc.--whatever sounds you have on your computer.