Apologies if I use wrong terms here, never been formally taught. Basically, I learned the basic of funtional harmony, which is the 3 funtions

Tonic Subdominant Dominant

I feel like I general get them. Tonic is easy, dominants like going to tonics, but still a little fuzzy on subdominant. Seems like they can kinda go wherever it's just that they create tension?

What I've been wondering about, and struggling to find info on that I can understand, is the depiction beyond this that includes different terms for each chord/note, like the mediant. I'm curious what each of these terms mean and what their general depiction is funtion wise. The only one I know of is the leading tone, which pushes you heavily back to the tonic, and that that's why the V and the viio are dominant, because they include the leading tone.

The rest is a mystery to me.