(Technically it's a motion, not a command. "i" as a command just enters insert mode.)
To elaborate, since this is one of my favourite vim features, say you have the following code:
do_something_with(some + long * complicated * expression)
* delete all the text between the two matching parens
* place you in insert mode with the cursor between the two (now adjacent) parens
* put the deleted text in the yank buffer so that 'p' will paste it.
The use case here is obviously so you can assign a name to that long complicated expression. 'ci)' is much easier than selecting it with the mouse, and keeps your hands on the keyboard where they belong ;)
With nested parentheses, it does what you expect (affects the text contained by the innermost matching pair to contain your cursor - try it and see).
Other equally useful variants:
* i" - "inside double quotes" - everything between double quotes
* i' - "inside single quotes"
* iw - "inside word" - the word the cursor is on
* is - "inside sentence" - great for editing prose
* ip - "inside paragraph"
There are also similar motions beginning with "a":
* a) - like i) but includes the parens (e.g. 'da)' deletes everything inside parens and the parens themselves)
* a" - similarly
* aw - like iw but includes trailing whitespace.
(Update - I thought this deserved its own air, so I turned it into a blog post: http://blog.samstokes.co.uk/post/767636740/vim-wizardry-1 Bonus tip if you read to the end!)
I've been using Vim for over a year and had no idea about this.
Holy crap, that's awesome.
My only regret is that I have but one upvote to give!
I always used to do F(lvf)hc rather than ci)