Ecological opportunity is any new niche that becomes available to species that wasn't available before. Adaptive radiations are common after mass extinctions, which leave a bunch of empty niches just waiting to be filled by new species. We have this type of opportunity to thank for our own evolutionary success. The major adaptive radiation of mammals occurred following the extinction of dinosaurs, leaving all that empty niche-space ripe for the taking.
Another cause of new ecological opportunity is when the organism changes, not the environment. There may be many unoccupied niches just waiting for species to fill them, but the organisms require a specific feature or characteristic in order to take advantage of them. A very basic example is the sea-to-land transition that happened for vertebrate animals some 375 million years ago. All the Earth's land was rife with ecological opportunity, but until a few basic features had evolved—like the ability to breathe and walk outside of water—life, at least for animals, was stuck in the oceans. The ability for animals to fly and plants to grow high opened the skies to life of all kinds. Then there was the evolved ability for hominids to walk upright and use iPhones. Maybe not that last one (yet). The world is full of opportunities. All it takes is a little bit of evolutionary innovation.
We have adaptive radiations to thank for some of the world's incredible biodiversity, as well as some classic evolution examples like the cichlid fish in African rift lakes. Lake Victoria alone has over 300 species of cichlid fish that arose via an adaptive radiation when the lake was formed. This happened in just 15,000 years—practically a blink of an eye. Cichlids also earned their marks as the poster children of speciation because those 300 species in lake Victoria all arose in sympatry. They arose by occupying different niches in the lake, and have remained separate species because they maintain strong reproductive isolation. This is despite their sympatry, which is often based on habitat use and mating cues.
It's a shame that plate tectonics are ripping East Africa into the Indian Ocean as we speak. In a few million years, salt water is going to rush in to all those lakes and wipe out the cichlids. Sigh.
Regardless of the cause—innovation or opportunity—there are some tricks to identifying an adaptive radiation:
1) The species in question must share a relatively recent common ancestor, meaning that many things speciated from one thing, and not that long ago. If the species don't share a recent common ancestor, then they're just a bunch of species living in the same place.
2) Each new species must have traits that are both 1) related to their different environments and 2) offer some fitness advantage in that environment. Another way of saying this is traits and environments are matched. If there are lots of traits, and lots of niches, but the traits have nothing to do with the niches, it's not adaptive radiation. In fact, we don't know what it is.
3) Lastly, the speciation has to be relatively fast. The idea behind adaptive radiation is that an evolutionary innovation or ecological opportunity allows for rapid speciation. If the process is slow, it's not usually considered an adaptive radiation.