The easy, non-theory explanation is it's the first few strings of a barre chord.
You only play the first few strings cause it sounds good on overdrive through an amp.
Like, hold a D barre chord and just play the 5th and 4th strings. (and possibly the third string as well ... depends on the song.) .. or just about any barre chord for that matter.
It also includes some open chords like E, A, G, D ... occasionally an open F but rarely an open C.
Each barre or open chord has it's individual reason for being a good power chord....again depending on the song.
An open E power chord is great cause it's got lots of bass and feeds back really well. An open A is easy to play with one finger and you can do some easy pull off leads to open strings. An open G, you can mute the 6th, and 5th strings (just playing strings 4, 3 and possibly 2) and then do harmonics on the 5th or 12th frets to get some good feedback harmonics.

Most beginner rock guys learn that it's easiest to learn most of your scales & riffs mainly in E and A cause there's lots of songs composed in those keys. You can learn all your leads on the 5th and 12th frets for a few months and then just transpose them to the other keys when you get used to playing them.

The basic secret to a power chord though is playing the first coupla strings of any barre chord so it sounds good through an amp. You can back up the root of any minor chords the keyboard player is holding down.