Reassortment is the mixing of the genetic material of two similar viruses that are infecting the same cell. In particular, reassortment occurs among influenza viruses, whose genomes consist of 8 distinct segments of RNA. These segments act like mini-chromosomes, and each time a flu virus is assembled, it requires one copy of each segment.
If a single host (a human, a chicken, or other animal) is infected by two different strains of the influenza virus, then it is possible that new assembled viral particles will be created from segments whose origin is mixed, some coming from one strain and some coming from another. The new reassortant strain will share properties of both of its parental lineages.
Reassortment is responsible for some of the major genetic shifts in the history of the influenza virus. Notably, the 1957 and 1968 pandemic flu strains were caused by reassortment between an avian virus and a human virus.
"Flu Vaccine Production Gets a Shot in the Arm". Ernie Hood, Environmental Health Perspectives Volume 114, Number 2, February 2006.