Imagine a stable ecosystem, full of plants and animals. The ecosystem is healthy, all the animals and plants are in their niches, surviving and getting along just dandy. Everything is in equilibrium.

Suddenly, something happens to disrupt this equilibrium; a volcano explodes, a river crashes through the forest and splits the ecosystem in two, a new disease or invasive species comes in, etc.

The ecosystem stability has been disrupted, just like a rock thrown into a still pond. The equilibrium has been punctured.

This creates a period of ecological "chaos", where the ecology gets re-organized. Maybe a plant that was once a food source is now being used for the breeding off an invasive insect, and this pushed out all the native animals who fed off the plant. Just an example.

During this brief period of chaos, as the ecology reorganizes itself to accommodate the changes, the local species will undergo rapid adaptation and evolution, as the altered environment is putting a strong selection pressure on them.

When the surviving species have adapted to fit into the new ecology, it will stabilize again into a new equilibrium. This can be 'punctured' again down the road by some new event, leading to a rapid burst of adaptations and evolution in the local species.