As far as I can tell, it makes some sounds louder and others quieter. Can someone explain with a metaphor or visual what it’s doing?
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You have it about right.
A good metaphor might be to think of a piano keyboard: there are 88 keys (typically) with those on the left controlling the longest strings with the lowest notes and those on the right controlling the shortest strings with the highest notes.
In a perfect situation, the piano is constructed to play every string at the same volume. In this perfect situation, the room is acoustically perfect, neither reflecting or absorbing certain notes more or less than any other. The listener in this situation also has perfect hearing, with no difficulty hearing any note. This allows the the performer perfect control over the music and is able to control how vigorously or how gently they play each note.
Alas, real life is rarely perfect. Rooms greatly affect sounds — think of how a large tiled bathroom sounds, or an elevator, or a spacious theater, or a shower stall. None of us have perfect hearing, especially those of us who are older or who listen to earbuds or who have used firearms without hearing protection. Hearing damage occurs unevenly, with some frequencies (some notes) being affected more than others.
Now add to that that when we use recorded music there are several steps that alter the sound. First, the recording changes the sound of the live performance. What microphones are used, how they are placed, what room was used for the recording, and a hundred other factors shape the sound in a certain way. Second, the medium used for playback affects the sound: a vinyl record sounds different than a CD, which sounds different than an MP3. Third, the musical equipment being used for playback affects the sound. Earbuds sound different than electrostatic speakers, which sound different than boomboxes. Every link in the chain changes something.
So there is a long, long list of factors that affect how our recorded piano sounds that make it different than what a live piano in the same room sounds like.
What the equalizer does is try to partially account for all of those changes by making precise changes to each frequency (each note). Maybe it pushes those higher notes up a little so we can hear them more clearly and so they shimmer like the notes from a real piano, and maybe it lowers the bass notes just a little to avoid a hollow boom caused by the placement of the speakers.
Some equalizers are very simple and some are tremendously complex but they all are designed to help shape the overall sonic spectrum to make music sound more lifelike.
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