A yo-yo consists of two similar lobes of material (typically plastic or wood) joined at their centres by an axle to which a length of string is attached.
Yo-yos generally are available in three basic forms: butterfly, tournament, and slimline. The butterfly models are, when viewed in profile, shaped somewhat like a butterfly (hence the name). The tournament design, the most popular by far, more resembles an Oreo cookie in profile. The slimline model is essentially a tournament with a smaller string spacing (think of an Oreo with no cream filling).
In theory, a yo-yos use is quite simple. Attach the free end of the string to your middle finger, wind the string about the axle of the yo-yo, hold the yo-yo in your hand above the ground and release. The yo-yo will fall towards the ground, spinning as it does. When it reaches the end of its string, it will wind itself back up the string, giving the raspberry to gravity all the while, and end up back in your hand.
In practice, however, operation is quite different. Some deal of manual dexterity is required to coax the yo-yo to return back up to your hand, and heaven help you if you actually want to catch it.