Descriptive notation is the old way of writing out chess games. In algebraic notation each square has one name but with descriptive they have two: one from white's point of view and the other from black's. This can make it kind of confusing. Black's perspective is in lower case only to make it easier to read.
Descriptive Notation
Black
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| QR8 | QN8 | QB8 | Q8 | K8 | KB8 | KN8 | KR8 |
| qr1 | qn1 | qb1 | q1 | k1 | kb1 | kn1 | kr1 |
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| QR7 | QN7 | QB7 | Q7 | K7 | KB7 | KN7 | KR7 |
| qr2 | qn2 | qb2 | q2 | k2 | kb2 | kn2 | kr2 |
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| QR6 | QN6 | QB6 | Q6 | K6 | KB6 | KN6 | KR6 |
| qr3 | qn3 | qb3 | q3 | k3 | kb3 | kn3 | kr3 |
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| QR5 | QN5 | QB5 | Q5 | K5 | KB5 | KN5 | KR5 |
| qr4 | qn4 | qb4 | q4 | k4 | kb4 | kn4 | kr4 |
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| QR4 | QN4 | QB4 | Q4 | K4 | KB4 | KN4 | KR4 |
| qr5 | qn5 | qb5 | q5 | k5 | kb5 | kn5 | kr5 |
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| QR3 | QN3 | QB3 | Q3 | K3 | KB3 | KN3 | KR3 |
| qr6 | qn6 | qb6 | q6 | k6 | kb6 | kn6 | kr6 |
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| QR2 | QN2 | QB2 | Q2 | K2 | KB2 | KN2 | KR2 |
| qr7 | qn7 | qb7 | q7 | k7 | kb7 | kn7 | kr7 |
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| QR1 | QN1 | QB1 | Q1 | K1 | KB1 | KN1 | KR1 |
| qr8 | qn8 | qb8 | q8 | k8 | kb8 | kn8 | kr8 |
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White
The pieces are written as follows,
K = King Q = Queen R = Rook B = Bishop
N = Knight P = Pawn
Descriptive is written out piece name first, a dash and then the square the peice is moving to. For the Scholar's Mate descriptive would look like this.
1. P-K4, P-K4
2. B-QB4, P-KR3
3. Q-KR5, P-QR4
4. Q-KB7 mate
Moves are written out in the easiest way possible as long as only one move is legal. For instance, if you're moving a bishop you don’t have to explain which bishop you are moving since there is only one bishop that can be moved. If two rooks can go to Q6, one being on Q8 and the other on Q2, you would write it out R/2-Q6 or R/8-Q6.
Kills are denoted with an "x", for instance NxQ, for a knight killing the queen. If two knights can kill the queen it follows the same rules as above, N/2xQ. Checks are written "ch" and checkmate is "mate". Castling is the same as algebraic 0-0 or 0-0-0 for a queen side castle. When queening a pawn a bracket is used, P-Q8(Q).
This system of notation is still found in the classic chess books but fell out of favor because it was more confusing than algebraic.