When people read the left bracket, they just say "kakko," but when they read the right bracket, they say "kakko-tojiru," which means "close bracket."
The fasten arcs are arcs that go around something to fasten these things all together. What are these things? They are (parentheses) and [brackets].
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own. Also, watch out from the shortening.