The beginning of a chess game is called the opening. In the opening, it is important to develop your pieces to good squares and control the center of the bourd. If you don't, and your opponent does, he can gain a significant advantage. However, if you can get a lead in the devopmental race, you will usually have the advantage. In this section, we will play though a common opening called the Ruy Lopez, and you will see why each move is strong.
1.e4 e5
White's move does two things: it controls the center with a Pawn, and it allows the Queen and f1-Bishop to get into the game. Black's move does the same things. Controlling the center gives your pieces more space on the board to move around in, while hindering the enemy from occupying good central squares. A spatial advantage is often a help in generating an attack. When you have a spatial advantage, you're often able to launch an attack against the enemy King, and his cramped position would would make it difficult for him to to defend.
2.Nf3 Nc6
White's move developed a Knight to it's best square, and it attacked Black's Pawn. This was a good move, because Black now has to defend the Pawn.
Black's move was also good. It defended his attacked Pawn, and it developed a Knight.
3.Bb5
This move defines the Ruy Lopez, and it puts pressure on the defending Knight. However, Black doesn't need to worry about it's capture, because after 3...a6 4.Bxc6 dxc6 5.Nxe5, he can play 5...Qd4 which forks White's Knight and Pawn. The Ruy Lopez is a widely used opening, and a favorite of many players with the white pieces. The activity that White gets from his first few moves is clear, because he is all set to castle next move, while Black still has his entire Kingside flank undeveloped.