Depth of Field
Depth of field refers to the range of distance from the camera lens where a subject will appear in sharp focus. Objects outside of the depth field will be blurry.
A narrow depth of field allows you to focus on a single subject and have it stand out in the foreground. Meanwhile, since the background will remain blurry, it won't pull attention away from the subject.
A key factor when keeping the backdrop out-of-focus is the size of the foreground subject in proportion to the physical format size of the camera image sensor. In order to obtain a small depth of field (and thus a defocused background), the camera's image sensor should be as large as possible in the physical sense - this has nothing to do with the number of megapixels. With a large enough image sensor, the depth of field can be adjusted using a diaphragm in the lens.
The frame-size in small analogue cameras has traditionally been 36x24mm. Such cameras allowed for very small depth of field with a wide-open diaphragm, e.g. f/2.0. Using such settings, depth of field would only span 10 centimeters in each direction from the center of focus.
Modern digital cameras feature ever-smaller sensors, making it increasingly difficult to achieve a small depth of field and a subsequently defocused backdrop.
Digital reflex cameras have sensors, often referred to as APS-Cs, that are half the size of an analogue frame or even somewhat smaller. Such sensors also allow one to achieve the artsy effect of defocusing the backdrop, though to a lesser extent than analogue cameras. Special attention should be paid to the size of the lens diaphragm when selecting a digital reflex camera. It's best to find one able to achieve an aperture of less than f/3.5, as larger values (i.e. smaller aperture openings) lead to increased depth of field and hinder ability to keep the background defocused.
On the other hand, compact cameras have extremely small sensors, and their size is usually given in fractions of an inch, e.g. 1/2.5". A small sensor means a nearly infinite depth of field, making a defocused backdrop nearly impossible to achieve with compact cameras.