Use round brackets (aka parentheses)

for additional information or explanation

1) To clarify or inform.
Jamie's bike was red (bright red) with a yellow stripe.

2) For asides and comments
The bear was pink (I kid you not).

Use square brackets

for editorial information, etc

1) To amend or supplement the given details
His first book [The Colour Of Magic] was written in 1989.

2) To replace phrases for clarity or brevity
[The treaty] decreed that no bear should be painted pink.