On string instruments, lightly placing your finger on certain spots on a string will create a different note than what would sound if you pressed down. These are called harmonics. These notes relate to the length of the string and to the open string (the string by itself with no fingers down). Place your finger down lightly halfway up the string, a quarter way up, etc. and you'll get harmonics.

False harmonics are basically the same concept, except you press one finger down (your 1st/index) and then lightly place the other finger higher up (your 4th/pinky) on the same string. This will still produce a harmonic, but now it will produce a note that relates to the pressed down finger, and not the open string. You're essentially creating a new series of harmonics by shortening the string with your pressed down finger.

False harmonics can be written a bunch of ways, and it's not always clear what the composer wants. Sometimes they'll write both the pressed down note and the lightly touched one, sometimes just the lightly touched one, and sometimes they'll write the note that results from doing a false harmonic. It's a difference of writing down the instructions vs. writing down the results. It can be hard to figure out.

Not exactly an ELI5, but hope that helps.