What is the "stonewall formation"? I use PyChess to play. It talks sometimes about how White or Black moved their pawns into "stonewall formation."

How do they do that, and what are the position's advantages/disadvantages?
Black usually reaches the Stonewall formation from the Dutch Defense (though QGD is an option as well, if he/she postpones Nf6) and involves putting pawns on c6, d5, e6 and f5. These pawns guarantee a strong grip on the light squares in the center (especially e4, which is often occupied by a knight later on), but weaken the dark squares. Another problem for Black is the light-squared bishop, which is severely limited by its own pawns. A typical Stonewall position is the following:

[FEN ""]

1. d4 f5 2. g3 Nf6 3. Bg2 e6 4. Nf3 Be7 5. O-O O-O 6. c4 d5 7. Nc3 c6


It's hard for White to crack Black's center, but he has many options, of which my favourite is to exchange some pieces and take advantage of Black's bad bishop in the late middlegame and endgame.

As @user1583209 notes, if White tries to reach this formation it's called the  Stonewall Attack – see the linked question for more details.