Special Move 1: Pawn Promotion
Since a pawn cannot move backwards, what happens when it gets to the back row? It promotes! What this means is you move the pawn to the back row, select a Queen, Rook, Bishop, or Knight, and put that new piece on the square the pawn just moved two (and remove the pawn).
Special Move 2: En Passant
En Passant is a French term that means “in passing.” Basically, it means a pawn that tries to pass up another pawn can be captured.
When a pawn chooses to move 2-squares as its first move and it lands side-by-side with an opponent’s pawn, the opponent may capture the pawn that just moved as if it only moved 1-square.
The diagram shows the white pawn moving 2-squares from its starting square. The red arrow from the black pawn shows how black can capture En Passant.
The last rule of this special move is that if you wish to capture a pawn En Passant because your opponent just moved their pawn 2-squares and it ended up next to your pawn, you must do it on this turn. If you wait until later, you cannot make the capture.
Special Move 3: Castling
Castling is a special move in chess that allows you to get your king safe. There are 2-ways to castle. The first way is to castle Kingside and the other is to castle Queenside. Kingside is the half of the board the King’s start on. Queenside is half of the board the Queens start on. Castling is also the only move where you can move 2-pieces on the same move, where the King moves 2-squares instead of 1-square, and the Rook gets to hop over a piece (your King).
As you can see, both the White King and the Black King can castle either on the Kingside or Queenside.
As you can see, White decided to castle Kingside while black decided to castle Queenside.
However, there are a few rules to castling. First, you cannot castle if you are in check. Here, the black queen is checking the white King. Therefore, white cannot castle. You also cannot castle THROUGH check. So, the Black Bishop prevents the King from castling queenside as well, because you can't castle THROUGH check. Finally, White cannot think about castling Kingside because he moved his Rook.
If you move your king, you also cannot castle. The example shows the White King having moved forward. Even if he moves back to his original square, he cannot castle.