Head swapping is the act of removing the head from an animated character and replacing it with a different one. This is usually done for one of two reasons: cost and memory constraints (on video game consoles).
Artwork is expensive to produce, so by recycling characters' bodies and only having to draw new heads, studios can save time and money. Early game consoles also had quite limited amounts of memory and storage space for games, so by reusing the body, several characters could be produced with only minimal extra memory requirements. This technique is closely linked to the more common palette swap.
Perhaps the most famous use of the head swap is in Capcom's Street Fighter series. Since the player could not select their character in the original Street Fighter, the character controlled by the second player, Ken, was made identical to the first player's character Ryu with Ken's head, yellow armbands (instead of Ryu's red gloves), and lack of slippers being the only distinguishing graphical features (in addition to his red gi). From Street Fighter II and onward, Ryu's and Ken's fighting styles began to deviate from each other and other head swaps who used variations of their fighting style began to be introduced such as Akuma (in Super Street Fighter II Turbo), Dan (in Street Fighter Alpha) and Sean (in Street Fighter III). Another example is Cammy with Juli and Juni, or Roxy and Poison (Final Fight).
Head swapping is not the only method of reusing character sprites, as a graphic designer can also change other parts of the body, whether it'll be the character's arms, legs or torso, with new ones to create a new sprite. An example of this would be the final boss in Smash TV, MC Mayhen, who uses the same base sprite as the Mutoid Man, but with a different head and chest as well.
The Elder Scrolls IV: Oblivion (and games built off the same engine, such as Fallout 3) uses a similar technique in order to create the variety of characters necessary to fill the large area the game is set in. Although its characters are three dimensional, it uses sets of predefined bodies and combines them with heads randomly generated from its character customization program.
In Mike Tyson's Punch-Out!!, each opponent has a head-swapped counterpart, with the exception of King Hippo.