Level design is essentially, the creation of the game world. The processes involved are quite vast and requires careful planning on both the visual, technical and gameplay for the player.
An example of early level design and testing in a games production is white boxing of the level. This is used to help gauge a much better understanding of the level in a 3D form, from the 2D concepts. This allows for gameplay and interactivity to be tested at a basic level with or without finished assets and art work.
Interaction with the game world is an important factor when creating any game. It allows the player to feel more immersed into the game world and subtle details like glass breaking when the player shoots it or the use of dynamic physics when a player knocks over a can or bottle, these elements all come together to help the level in which the player is in.
Of course most game levels are in fact quite linear, and this is one of the areas that good level design can overcome and in a sense, lie to the player in giving them the impression they have a wide choice of areas to travel. A good example of this is Metal Gear Solid series. For example in MGS3, the game takes place in vast jungles and the player gets the impression they can explore and do there own thing. However, each level of the jungle usually had 1 or 2 ways out, which normally both lead into the next area, but gave the feeling of choice and exploration in the game, even though you were simply progressing the levels the way they intended.
A good reason as to why this was so effective, was the fact that the game level incorporated numerous routes around the level, but all funnelled into the end of the levels area.