What does the curl do? What does the curl do to the two notes that it connects? What does it mean? I tried googling curl with music notes but nothing relevant came up.
Slur is the word ! Or legato.It kind of joins the notes together. Imagine when you speak, the next word is almost joined to the last, without an audible gap. Or if the notes were played on a trumpet, they would be in the same breath, with no tonguing on the second note.
Sometimes a slur mark will go over several notes, telling the player that they will come out as a phrase - almost like a sentence - in one go, sequentially.
Not to be confused with a tie, which looks identical, but joins notes that are the same pitch.