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.
This is at least the third utterly basic question about music notation you ask (previous questions asked why some adjacent notes in a system were half steps and some whole steps, and what an augmentation dot after a notehead means).
There are a number of online as well as offline introductions into music notation that would make sense consulting before cluttering StackExchange with questions that do not improve the site since the same search terms you'd need for finding them will work fine with a web search, and you'll encounter all of them in any short introduction into notation anyway.