Depth of Field
Depth of Field is a term used to describe the distance between the first part of your picture which is in focus and the last. As a photographer you can control the depth of field with your lens selection and the aperture you choose.
The larger the aperture the shorter the depth of field, so you can for instance take a portrait picture of someone and the entire background will be out of focus where as the subject is crystal clear, you see these shots used widely in portraits and in the example picture used with this article where I focused to the right of a written sign with a narrow depth of field so the writing to the left of the sign is completely out of focus.
The smaller the aperture the larger the depth of field, so things at the front and back of the shot can be in focus simultaneously, ideal when taking shots of landscapes for example.
All lenses have an aperture range which is also known as the F number, if you are purchasing lenses to take specific types of shots make sure you do the research to ensure they do what you want them to!