Midi files are essentially digital "player piano" files - they play back a synth. Since they have no "sound" the files are small. I have a great dislike for downloaded midi files which are often poorly made and can contain lots of garbage in many forms. If you can't make your own then you can buy professionally-made commercial midi files from a number of sources. Or you can create your own pretty easily with a program called Band In A Box from http://www.pgmusic.com/.

Playing back midi files and using an arranger are two different things really - an arranger follows your chord input live whereas a midi file on playback does not. Midi file playback requires a sequencer or midi player... there's many ways to accomplish this from using keyboards to dedicated midi file players or computers.