[ 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 have to be implemented that way, but a [ without a matching ] would have made a lot of people very very nervous.)