[ is actually a command, equivalent (almost, see below) to the test command. It's not part of the shell syntax. (Both [ and test, depending on the shell, are often built-in commands as well, but that doesn't affect their behavior, except perhaps for performance.)
An if statement executes a command and executes the then part if the command succeeds, or the else part (if any) if it fails. (A command succeeds if it exits with a status ($?) of 0, fails if it exits with a non-zero status.)
In
if [ "$name" = 'Bob' ]; then ...
the command is
[ "$name" = 'Bob' ]
(You could execute that same command directly, without the if.)
In
if grep -q "$text" $file ; then ...
the command is
grep -q "$text" $file
man [ or man test for more information.
FOOTNOTE: Well, the [ command is almost equivalent to the test command. The difference is that [ requires ] as its last argument, and test does not -- and in fact doesn't allow it (more precisely, test doesn't treat a ] argument specially; for example it could be a valid file name). (It didn't test0 to be implemented that way, but a [ without a matching ] would have made a lot of people very very nervous.)
The square brackets are a synonym for the test command. An if statement checks the exit status of a command in order to decide which branch to take. grep -q "$text" is a command, but "$name" = 'Bob' is not--it's just an expression. test is a command, which takes an expression and evaluates it:
if test "$name" = 'Bob'; then ...
Since square brackets are a synonym for the test command, you can then rewrite it as your original statement:
The best way to think of the [ ... ] syntax, is to consider [ to be a program - which it is!
Check this out:
~ $ ls /usr/bin/\[
/usr/bin/[
on the other hand, you're probably not using that version of it since bash also provides [ as a shell built-in.
Anyway, to answer your question: What if does is run the command you give it and see it the return value is 0 or not. You use [ to do other, more interesting comparisons such as string comparisons. See man [ and man bash.