Adaptive radiation is said to have occurred when an adaptive zone that is (or has become) vacant caused the ancestral species to diversify into a variety of related forms within a relatively short period of time. Each of them is adapted to fit to a particular environmental niche.
The common example of adaptive radiation is the honeycreepers in Hawaii. Since Hawaii is an island, there were fewer birds (thus, fewer competition for food) while several adaptive zones were available. Some of them evolved and had firmer, smaller beaks to rip away bark for insects; others had longer, curved beaks to sip nectar from tubular flowers.