It's Descriptive Notation.
Each square is named after the piece that occupies it.
a1 would be QR1 or Queen's Rook 1.
a2 would be QR2 or Queen's Rook 2.
etc
b1 would be QN1 or Queen's Knight 1.
c1 would be QB1 or Queen's Bishop 1.
d1 would be Q1 or Queen 1.
e1 would be K1 or King's 1.
etc.
The tricky part is black's notation is the same.
e8 would be K1 for black (or K8 for white)
If white plays pawn to e4 it would pe P-K4.
If black put a pawn on that same square, the black notation would read P-K5 (it is black's king 5 square).
A pawn capture like exd5 would read PxP (or pawn takes pawn).
If there is more than one capture, it would read PxQP (or pawn takes queen pawn).
Here is a test.
Play out this game
1.P-K4 P-K4
2.N-KB3 P-Q3
3.P-Q4 B-N5
4.PxP BXN
5.QxB PxP
6.B-QB4 N-KB3
7.Q-QN3 Q-K2
8.N-B3 P-B3
9.B-KN5 P-N4
10.NXP PXN
11.BXNP+ QN-Q2 (Queen's Knight to Queen 2 ... The Queen's Knight Starts out on b8)
12.0-0-0 R-Q1
13.RXN RXR
14.R-Q1 Q-K3
15.BXR+ NXB
16.Q-N8+ NXQ
17.R-Q8 Mate
I played this game out from memory. hehe
Here it is in alebraic with a PGN Window.
1. e4 e5 2. Nf3 d6 3. d4 Bg4 4. dxe5 Bxf3 5. Qxf3 dxe5 6. Bc4 Nf6 7. Qb3
Qe7 8. Nc3 c6 9. Bg5 b5 10. Nxb5 cxb5 11. Bxb5+ Nbd7 12. O-O-O Rd8 13. Rxd7
Rxd7 14. Rd1 Qe6 15. Bxd7+ Nxd7 16. Qb8+ Nxb8 17. Rd8#
{White mates} 1-0
Test:
Name this square from white and black's point of view.
e5 Answer White: K5 Square Black: K4 Square
f6
h7
d5
1.NXN What just happened?
1.PXP e.p. What just happened? (Tricky)
1.P-QN8 What did white just do?
I hope this helps.