Descriptive Chess Notation is a notation for recording chess games, and at one time was the most popular notation for doing so. Alternate names for this notation include descriptive notation, English notation, and English descriptive notation. It is not used often today (most people today use algebraic chess notation), but is still important for understanding older textbooks on Chess.
Each move in descriptive chess notation is either a special castling symbol (O-O for a kingside castle or O-O-O for a queenside castle, as with algebraic notation), or by the following sequence: piece name, "-" (no capture) or "x" (capture), its final square at the end of the move, and special indicators if any. The piece names are K (King), Q (Queen), R (Rook), B (Bishop), Kt (Knight), and P (Pawn); note that English versions of algebraic notation use the same abbreviations except for the Knight and Pawn. Special indicators include e.p. (en passant), Ch (Check), and Mate (Checkmate). If the move is a capture, the final square may be indicated by naming the piece being captured rather than by naming the final square. Typically, the move will record only enough information to make the move unambiguous, and piece names may be combined with a location to eliminate ambiguity. So, depending on the available possibilities, a pawn capturing a pawn may be noted as "P x P" if that is the only capture possible, or as "QBP x QP" ("Queen's Bishop's Pawn captures Queen's Pawn") if more than one such move is possible.
The primary difference between algebraic and descriptive notation is how squares are specified. The squares are identified by what piece originally starts there (using the adjectives "Queen's" and "King's" to disambiguate the side), followed by how many squares from that player's perspective. Thus, when White is playing, algebraic notation's square "a1" in descriptive notation would be spoken as "Queen's Rook 1" and written as "QR1" in descriptive notation. Squares written as a1 through h1 in algebraic notation are written in descriptive notation as QR1, QKt1, QB1, Q1, K1, KB1, KKt1, and KR1. From White's perspective, the square notated as "e4" in algebraic notation is described as "K4" in descriptive notation. Note that the name for the same square has a different representation depending on whether the player is Black or White; the square notated as K4 for White is notated as K5 for Black.
Thus, moving the King's pawn forward two squares as an initial move would be written as "e4" in algebraic notation, and as "P-K4" in descriptive notation.
Algebraic notation has the advantages of representing the same moves with fewer characters (on average), and using the same representation for the same location regardless of player.