The main idea here is that Black succumbs to a peep from White.
In such a shape, it's not uncommon for Black to peep:
$$Bc
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . , . , . , . . |
$$ | . . . W . . . . . |
$$ | . . , a 1 . , . . |
$$ | . . . W . . . . . |
$$ | . . , . , . , . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+
- Click Here To Show Diagram Code
[go]$$Bc
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . , . , . , . . |
$$ | . . . W . . . . . |
$$ | . . , a 1 . , . . |
$$ | . . . W . . . . . |
$$ | . . , . , . , . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]
White typically connects solidly at
a, and is strengthened. Peeps are usually a tactical move used to get an outcome that outweighs the strengthening of White. As EdLee pointed out, Black's next move if White ignores the peep will be to push through at
a himself (following up on the original threat). This leads to a poor shape for White, with cutting points.
$$Wc
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . , . , . , . . |
$$ | . . . 1 . . . . . |
$$ | . . , a B . , . . |
$$ | . . . W . . . . . |
$$ | . . , . , . , . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+
- Click Here To Show Diagram Code
[go]$$Wc
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . , . , . , . . |
$$ | . . . 1 . . . . . |
$$ | . . , a B . , . . |
$$ | . . . W . . . . . |
$$ | . . , . , . , . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]
Now what's bad about the diagram above is that where the Black stone is simply there to start with, White

has turned it into a peep against his shape
on his own turn. Now he does not have time to avoid Black cutting at
a. The fact that White has given Black this opportunity by making Black's stone into a peep without making black expend a turn is a big difference from the first diagram.
Now Black can push through and cut at any time, and White still has to spend a turn to defend at
a. If

doesn't achieve something big, it might have been better at
a to begin with.