A good general definition of ex-situ conservation is “off-site conservation,” or a method of conservation that can be done outside the natural habitat. Examples include sperm and egg banks as well as zoos and botanical gardens, as the previous answer suggested.
Ex-situ conservation is meant to help species keep a healthy population by removing them from predators and other conditions that could lead to poaching, extinction, etc.
However, there are some drawbacks to this. Whatever is being conserved this way has to be able to survive the new conditions. It often leaves several very localized species at risk or in danger of extinction. Often, endangered species are not good candidates for this kind of conservation, leaving them in danger of going extinct.