Forsyth-Edwards Notation (FEN) describes a chess position. In a single line of ASCII text, it describes all the information about the state of a game.
Here is an example FEN string: 8/5N2/4p2p/5p1k/1p4rP/1P2Q1P1/P4P1K/5q2 w - - 15 44
And here is the position it describes:
Breaking down our example FEN string a bit:
castling ability
| en passant target square
| |
| | fullmove counter
v v v
8/5N2/4p2p/5p1k/1p4rP/1P2Q1P1/P4P1K/5q2 w - - 15 44
| | ^ ^
------------------------------------- | L halfmove clock
|__ piece placement |
Side to move (white)
This is the BNF grammar that describes the FEN notation:
<FEN> ::= <Piece Placement>
' ' <Side to move>
' ' <Castling ability>
' ' <En passant target square>
' ' <Halfmove clock>
' ' <Fullmove counter>
<Piece Placement> ::= <rank8>'/'<rank7>'/'<rank6>'/'<rank5>'/'<rank4>'/'<rank3>'/'<rank2>'/'<rank1>
<ranki> ::= [<digit17>]<piece> {[<digit17>]<piece>} [<digit17>] | '8'
<piece> ::= <white Piece> | <black Piece>
<digit17> ::= '1' | '2' | '3' | '4' | '5' | '6' | '7'
<white Piece> ::= 'P' | 'N' | 'B' | 'R' | 'Q' | 'K'
<black Piece> ::= 'p' | 'n' | 'b' | 'r' | 'q' | 'k'
<Side to move> ::= {'w' | 'b'}
<Castling ability> ::= '-' | ['K'] ['Q'] ['k'] ['q'] (1..4)
<En passant target square> ::= '-' | <epsquare>
<epsquare> ::= <fileLetter> <eprank>
<fileLetter> ::= 'a' | 'b' | 'c' | 'd' | 'e' | 'f' | 'g' | 'h'
<eprank> ::= '3' | '6'
<Halfmove Clock> ::= <digit> {<digit>}
<digit> ::= '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'
For more information about what all these thinngs mean, check out the Forsyth-Edwards Notation page on the Chess programming wiki