Ex vivo is a term used in reference to the study or assay of living tissue in an artificial environment outside the living organism. The opposite of "in vivo," meaning to take place inside an organism,"ex vivo" is a simple compliment to the contrary of this oft used word in the life sciences as well as other fields.
Ex vivo studies are usually performed "in vitro", or in the lab; although the use of these two words is not dichotomatory. Ex vivo studies can certainly occur "in vivo," or inside an organism or system. This would mean, though, that the object of interest is placed inside of another--this is not very practical, although some might find a clever manipulation of such a procedure.
One of the widely used ex vivo studies is the Chicken chorioallontoic membrane assay or simply CAM assay. For example, in this assay, angiogenesis is promoted on the CAM membrane iside a fertilized chicken egg. Hence, this assay studies the living tissue (or membrane) outside an organism (chicken).