How to quickly remove a pair of parentheses, brackets, or braces in Vim?

One can take advantage of the text objects that are built in into Vim
(see :help text-objects). The desired edit can be stated as a
sequence of the following three actions.

1. Cut the text inside the square brackets:

    di[
   

2. Select the (empty) square brackets:

    va[
   

   Alternatively, you can just select the character under the
   cursor and the one to the left of it, because the command
   from step 1 always puts the cursor on the closing bracket:

    vh
   

3. Paste the cut text over the selected brackets:

    p
   

Altogether, it gives us the following sequence of Normal-mode commands:

di[va[p

or, when the alternative form of step 2 is used:

di[vhp