A lot of learning and playing music is about communication of intent between musicians. (not the same as performing for the audience).
Because of this, musicians have to develop methods to quickly convey to other musicians what to play, when to play, how loud… So we end up with music notation. So with music notation, and because many musical patterns are very commonly used throughout music, we end up with “shorthand” or quick ways to name and communicate musical stuff.
One very common shorthand are chords. So rather than saying play note C, E and G, I could say play Cmajor (chord) and musicians know this means notes C,E,G. Within a song, there tends to be a common scheme of chords that “work well” for most melodies. For example pop songs in C major scale usually have Cmaj, Gmaj, Amin, Fmaj chords played sequentially. This is a chord progression. Another shorthand way to say this is C major scale, play the 1, 5, 6, 4 chord progression since G is the 5th note, A is the 6th note and F is the 4th note in the C major scale.
A lot of popular and classical music uses a common scale pattern so these chord progressions are just an easy way to communicate what to play very quickly (which is especially useful for piano and guitar because these instruments can play multiple notes at the same time and writing down each note can be hard to read)
There is a lot of theory behind why some progressions work and why they invoke a certain feeling or movement to the music but that would be way beyond ELI5. Bottom line: chords and chord progressions are shortcuts for quick communication between musicians.
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