The game of baseball is played on a baseball field. Another name for the baseball field is the "diamond" because of the shape of the infield.
Here is a diagram of the baseball field:
Author: Robert Merkel via Wikimedia, pd
The Infield
The infield is the area from the grass line in to home plate. It includes all the bases and is where most of the action in the game of baseball takes place.
Bases
The bases are perhaps the most important part of the baseball field. There are four bases: home plate, first base, second base, and third base. The bases form a diamond or square starting with home plate. While standing at home plate and looking at the picture, first base is 90 degrees to the right and 90 feet away. Third base is to the left and second base is between first and third. All the bases are 90 feet apart for Major League baseball. For little league baseball they are 60 feet apart.
Pitcher's Mound
In the middle of the infield diamond is the pitcher's mound. This is a raised area of dirt with a pitcher's rubber or plate in the middle. Pitchers must keep their foot on the rubber when throwing a pitch. The pitcher's rubber is 60'6" from home plate in the majors and is 46 feet from home plate in little league.
Fair and Foul
The first base and third base lines extend from home plate all the way to the outfield fence. These lines determine if a hit is fair or foul. The area between (and including) the foul lines is fair territory, while anything outside them is foul.
Batter's Box
The batter's box is an rectangle on each side of the plate. Batter's must be in the batter's box when they hit the ball. If you want to leave the batter's box, you must call time out and get permission from the umpire or you may be called out. If you step on the line or out of the box when you hit the ball, you will be called out.
The batter's box is 4 feet wide by 6 feet long in the Major Leagues. It is generally 3 feet wide by 6 feet long in little league and some youth leagues may not have the lines drawn out.
Catcher's Box
The catcher must be in the catcher's box during a pitch. It is a balk if the catcher leaves the box before the pitcher releases the pitch.
Coach's Box
Next to first and third bases are coach's boxes. Generally a coach can stand in these boxes to help the base runner or to pass signs on to the hitter. Coaches may leave the boxes as long as they don't interfere with play.
On Deck Circles
These are areas where the next batter up may warm up and get ready to hit.
Outfield
Between the grass line and the home run fence is the outfield. This is a large area covered by three players. The distance to the home run fence, or outfield wall, is not set by the rules and varies from ballpark to ballpark. In major leagues the fence is generally around 350 to 400 feet from home plate. In little league, it is usually around 200 feet from home plate.