Yes but what is pawn on g7 do?
What is the concept of a weak square?
One principle that the article did not mention explicitly is that just like pawns that have to be defended by a piece instead of by another pawn create weaknesses. Squares on your own side of the board that have to be defended by a piece instead of your own pawns creates weaknesses. Notice I wrote weaknesses. This is to make you aware of another principle: The Principle of 2 Weaknesses.

Yes sorry I was away for a bit.
Back on the topic of weak squares, I have another query:
How can the defending side shore up a weak square?

Is it inherent in certain squares, or does it go by what piece is placed near?
A weak square is a square that cannot be defended by a pawn.

Is it inherent in certain squares, or does it go by what piece is placed near?
A weak square is a square that cannot be defended by a pawn.
This is the best answer John, and by definition, cannot be fixed because pawns cannot go backwards.

One principle that the article did not mention explicitly is that just like pawns that have to be defended by a piece instead of by another pawn create weaknesses. Squares on your own side of the board that have to be defended by a piece instead of your own pawns creates weaknesses. Notice I wrote weaknesses. This is to make you aware of another principle: The Principle of 2 Weaknesses.
There is a lot of truth in what YaroSlavl said. Keep in mind also, a weak square can also be an exploitable square for an outposted knight, as can it be a useable square for the opponent to your disadvantage with any piece. One thing I like to keep in mind is there is also a belief that a weakness that cannot be exploited isn't necessarily a weakness. That isn't a universal concept though. What I mean is, as long as a player has enough activity and is able to produce threats of his own, then that belief can apply, but as the game goes on, and more and more pieces start coming off the board, the weakness may become quite tangible.
The point of a weak square is so that you are more cautious in not creating them, there is no such thing as making them unusable once they are created. You can try to control them with pieces instead of pawns I guess.

One principle that the article did not mention explicitly is that just like pawns that have to be defended by a piece instead of by another pawn create weaknesses. Squares on your own side of the board that have to be defended by a piece instead of your own pawns creates weaknesses. Notice I wrote weaknesses. This is to make you aware of another principle: The Principle of 2 Weaknesses.
There is a lot of truth in what YaroSlavl said. Keep in mind also, a weak square can also be an exploitable square for an outposted knight, as can it be a useable square for the opponent to your disadvantage with any piece. One thing I like to keep in mind is there is also a belief that a weakness that cannot be exploited isn't necessarily a weakness. That isn't a universal concept though. What I mean is, as long as a player has enough activity and is able to produce threats of his own, then that belief can apply, but as the game goes on, and more and more pieces start coming off the board, the weakness may become quite tangible.
Not sure if the OP is serious in his request, but this is a good point. Chess is a very dynamic game. What is "weak" isn't always easy to define. Nearly every time someone says a square is weak, they're implicitly saying it's also attackable, and that controlling the square is worthwhile.
But what's attackable or worthwhile in one position isn't always in another. Furthermore, something seemingly attackable may not matter due to counterplay or initiative in the specific position... and it may be as little difference as whose move it is. IQPs are an easy example of a set of weaknesses being debated by both players.
But anyway, other than the theory of it, a bit of useful advice is that often a weak square is useful because you use it to attack more concrete targets. An easy example is infiltration with a rook on c7 to attack pawns on the 7th rank, or a knight on f5 to attack the black king. In the case of IQPs, occupying the square in front immobilizes the target. Off the top of my head, outposts and blockading are the two main uses of weak squares.

The OP asked what is a weak SQUARE, not about weaknesses in general.
I_Am_Second gave the precise definition in post #7.
Instead of listening to us hacks, read the link posted by LongIsland Mark as well as these articles by IM Silman on weak squares (and a few other things):
http://www.chess.com/article/view/you-have-it-he-doesnrsquot-part-1
http://www.chess.com/article/view/you-have-it-he-doesnrsquot-part-2

Except that sometimes a weak square can be defended by a pawn
But that's not a bad definition to start with.

Yeah, a hole it's a good example, but doesn't give you the concept of a weak square.
Silman does a good job of bypassing concepts beginners use as pseudo-useful crutches and talks about concepts in a way that they're actually useful. "you have it, he doesn't, now do something with it" is a nice way to put it.
Is it inherent in certain squares, or does it go by what piece is placed near?