Convergent evolution is the driven by natural selection, the mechanism for evolution. Evolution is the change in gene frequencies within a population. This requires individuals within a population to have different phenotypic expressions of traits. Some of these variations of traits grant more reproductive opportunities to those that possess them; for example they may be stronger, faster, or more attractive to the opposite sex. If those traits are then inherited by the offspring, they will become more common within the population. On the other hand, some variations of traits will reduce/eliminate reproductive success for those that possess them and those genes will decrease in the population, as a whole, through time. This interaction between genes and the environment results in the changes in gene frequency within a population.
In geographically separate but similar environments, evolution may be driven by a similar selective agent. For example, in desert ecosystems around the world, heat is a ubiquitous, strong, selective agent that is capable of killing individuals that do not possess adaptations to its power (thus eliminating their genes from the population and favoring the spread of other genes that allow survival at high temperatures).
The possible adaptations to heat are limited by physiological realities, ancestral histories, and physical laws. A desert rodent can not survive by ignoring the physical law that its protoplasm will coagulate at a high enough temperature. It can aestivate, become crepuscular/nocturnal, or resort to subterranean life. There are a limited number of adaptive solutions to any given selective agent. This leads to convergence. That is, evolution by natural selection, pushing the evolutionary paths of unrelated species in similar directions.
The limited solutions to selective agents frequently lead to convergence of a trait. Consider the similarities amongst unrelated aquatic life forms (e.g. a penguin, a fish, and a...