It's simple and cool...a Chess board has 64 squares, and when you want to tell your friend that you found a chess game amazing and describe what happened in the game, your friend would be confused if you tell the king moved here and queen moved there and the bishop took knight and rook took queen, because it's hard for you to tell which of the 64 squares the queen started moving from, and which of the 63 it lands on! Also, there are 2 bishops, 2 knights, 2 rooks, and 8 pawns to make matters worse, since your friend won't understand which of the 8 pawns are you talking of!
A simple and well accepted notation exists to solve this problem, you assign a label for each square and an alphabet in upper case for each piece, and viola! You suddenly start explaining games to your friend without any ambiguity!!
The first column of the chess board as seen by you when you play white is called a(starting from left and going to your right), next is b, the third is c, and so on till 8th column, which is h. The first row closest to you is 1, second is 2, and so on till eighth, with is 8. So now, when you play white, the closest square to you to your right is h1, while the leftmost one closest to you is a1.
Next the pieces, queen is represented by Q, rook by R, knight by N, bishop by B, king by K, and pawn has no letter for it. So to answer your question now, g4 means a pawn has moved to the square g4, so is the case for e5 and f3. Qh4 means the queen has moved to h4 square.
Hope my answer helped, cheers!:)
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