Chimerism is a very rare condition caused by the fusion of zygotes (fertilized eggs) into a single form during early cell duplication. It is extremely rare, with only forty or so known human cases. It is somewhat more common in the animal kingdom.
Once an egg cell has been fertilized by a sperm cell, it imbeds in the wall of the uterus and starts to develop. Since the egg is microscopic at this point, the uterus has more than enough room to accommodate fraternal twins - two fertilized eggs. However, on very rare occasions, the eggs will embed themselves quite close to each other. In some cases, one growing zygote will absorb the other one, creating one being with two different DNA coding sequences. Generally, one of the sequences will dominate and form most of the body's tissues. However, cells from the other zygote may continue to duplicate and spread throughout the body, creating body tissues in the right place, but with different DNA.
Complications depend on where the foreign DNA presents itself. Because the immune system will often see this tissue as natural, it will not attack it the way it would otherwise attack foreign tissue. However, it may not function normally, or may function unpredictably.