Plankton are microscopic plant and animal organisms that float in huge numbers in fresh or salt water. "Phyto" comes from a Latin word meaning tree or plant. So phytoplankton are the tiny, plant-like algae drifting in fresh or sea water. These organisms reproduce in two ways -- asexual or sexual.
Asexual reproduction occurs with just one parent, instead of the usual male/female method of reproduction. Fision is the most common and simplest form of asexual reproduction. It occurs when a single-cell alga divides into two new cells. Each new cell takes half of the original parental cell and forms the missing half on its own. Another form of asexual reproduction happens when phytoplankton shed spores. These spores are usually single-cell structures, and they can also grow into new organisms by themselves, with no fertilization. Finally, some phytoplankton reproduce asexually using a method called fragmentation. This is when several segments of a filament (the parent) break away, forming a fragment. Through cell division, the fragment is able to grow into a new filament.
Some phytoplankton reproduce sexually, when two specialized reproduction cells fuse (similar to reproduction in humans). This occurs two different ways: with two cells from the same phytoplankton (seen in plankton called monoecious) or with two cells from two different phytoplankton (in plankton called dioecious). The two cells fuse during the fertilization process. For simpler forms of phytoplankton, the simple fusion process produces a zygospore. In more advanced types of phytoplankton, the more complicated fusion process produces a zygote. Both the zygospore and the zygote then grow into mature phytoplankton.