When is it proper to use the squared brackets on the computer's keyboard?

I use them for arrays when programming.

For example in Ruby.

ary = [1, “two”, 3.0] #=> [1, “two”, 3.0]

When talking about the Apple ][ or Apple ][ plus computers

They are secondary parentheses. For example:

Find all three keys [blue key (north room), green key (east room), yellow key (south room)] and proceed to the Boss Chamber.

I love Wikipedia.

There’s a whole section near the top of the page to explain it better than I was about to attempt, and then more “special uses” at the bottom of the page.

I was going to say for initializing an array – something covered under @johnpowell‘s answer.

They also have a mathematical meaning. When listing a range of numbers, if it’s in square brackets, (e.g. [4, 8]) the end points are included in the range. Most people would probably just write that as 4–8, but for mathematical purposes sometimes extra precision is necessary.

BBc codes for simple text editing: [italic]test[/italic] works on a lot of forums.

It allows members to edit text without the potential malicious damage that could happen if members were allowed to use HTML in their posts.

They are used in programming…usually for arrays.

In writing, sometimes you need parenthesis inside parenthesis, and you’d use the square ones inside the regular ones. Like so: Blah blah blah (not to mention rah rah [easily forgotten] and yah yah).

For adding or replacing text in a quote to make it more clear.

Example: I was reading a Fluther question about square brackets and I read that, ”[Hawaii_Jake] can’t find any rules for their use.”

How to Cite when you are Altering a Direct Quote

You’re stupid if you don’t use them when somebody writes, “Your [ sic ] stupid.