Low pincers are on the 3rd line (from the edge, so a/c/e in jlt's diagram), high are on the 4th line (b/d/f). A pincer is a move on the other side of the opponent stone from where your existing stone(s) are: you are approaching it from 2 sides, like a
pincer movement in a battle.
So

here is a pincer: black has stones on either side of white

. The main strategic thing a pincer does is make it hard for the pincered stone to extend along the side in the direction of the pincer to make a base (space for eyes and thus safety) in that direction.
$$B
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$$ | . . . 1 . . . . . , . . .
$$ | . . . . . 2 . 3 . . . . .
$$ | . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . .
$$ +--------------------------
- Click Here To Show Diagram Code
[go]$$B
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$$ | . . . 1 . . . . . , . . .
$$ | . . . . . 2 . 3 . . . . .
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$$ | . . . . . . . . . . . . .
$$ +--------------------------[/go]
Compare to if black just answered with patient knight move

, white could extend on side to make a base:
$$B
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$$ | . . 3 . . . . . . . . . .
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$$ | . . . 1 . . . . . , . . .
$$ | . . . . . 2 . . 4 . . . .
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$$ | . . . . . . . . . . . . .
$$ +--------------------------
- Click Here To Show Diagram Code
[go]$$B
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$$ | . . 3 . . . . . . . . . .
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$$ | . . . 1 . . . . . , . . .
$$ | . . . . . 2 . . 4 . . . .
$$ | . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . .
$$ +--------------------------[/go]
A counter pincer is a move which pincers the pincer

So

could be described as a counter-pincer, because it pincers

with

and

. It stops

from extending along the side around there to make a base. But it didn't help

and is separate from it so black could just link up at
a to make his stones safe.
$$B
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$$ | . . . 1 . a . . . , . . . . . , . . . |
$$ | . . . . . 2 . 3 . 4 . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
- Click Here To Show Diagram Code
[go]$$B
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$$ | . . . 1 . a . . . , . . . . . , . . . |
$$ | . . . . . 2 . 3 . 4 . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
So if white wants to attack

it is important to separate it from

first. So white could jump out, black probably defends at

(or one to left) and then white can counter-pincer at

and

can't connect to

/

. With these kind of pincer and then counter-pincer moves it is common for running fights to develop, with both players having groups which are weak.
$$B
$$ | . . . 5 . . . . . . . . . . . . . . . |
$$ | . . . . . 4 . . . . . . . . . . . . . |
$$ | . . . 1 . . . . . , . . . . . , . . . |
$$ | . . . . . 2 . 3 . 6 . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
- Click Here To Show Diagram Code
[go]$$B
$$ | . . . 5 . . . . . . . . . . . . . . . |
$$ | . . . . . 4 . . . . . . . . . . . . . |
$$ | . . . 1 . . . . . , . . . . . , . . . |
$$ | . . . . . 2 . 3 . 6 . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]