Fraternal twins which have different fathers. The mother produces two eggs, but they are fertilized by sperm from two different males.
We have very little idea how common this is, as it can usually only be discovered through genetic testing. It had long been known to be possible, even before the event of modern genetic testing, through a few rare cases of a mother having one twin by a black man and one by a white man. It is suspected that for this to happen the mother must have sex with both men in a matter of hours, or less, otherwise both eggs would be fertilized by the first man's sperm.
Genetically, the twins will share 25% of their DNA (half-siblings).