Curly brackets (so-called in British English; North American English prefers braces) are sometimes used in prose to indicate a series of equal choices: “Select your animal {goat, sheep, cow, horse} and follow me”. They are used in specialized ways in poetry and music (to mark repeats or joined lines). The musical terms for this mark joining staves are “accolade” and “brace.” In mathematics they delimit sets. In many programming languages, they enclose groups of statements.

RE:
What do you call this symbol { } ?
I thought they were called brackets, but my algebra 2 teacher said they're not. Anyone know what those squiggly bracket things are called?

These are [ ] brackets and these are ( ) parenthesis.