Descriptive notation is an older form of chess notation that was widely used to describe chess games before the advent of the algebraic system. Since being replaced it's usage has been largely curtailed.
Every square has 2 names under this system, one from White's point of view and one from Black's. The ranks are still numbered 1-8 with rank 2 from White's point of view considered as rank 7 from Black's.
The files instead of being labeled as letters a-h are described as follows: a=QR, b=QN, c=QB, d=Q, e=K, f=KB, g=KN, h=KR. Fortunately due to the symmetrical nature of the chess set-up, the files are the same for both sides.
A pawn move recorded under algebraic notation as 1.e4 would read as 1.P-K4. 12...Bg4 would read 12...B-KN5. If a Bishop captures a Knight for example it is recorded simply as BxN. Castling is the same as algebraic and a pawn promoting to Queen on b8 for example can be written as P-QB8(Q), P-QB8/Q or even P-QB8=Q.