Metastability has slightly different meanings in different fields of knowledge. The general idea, however, is that something is metastable if it is not changing, yet given a small force ("nudge") it will transition to another, more stable state.
For example, a block is sitting on a slope (an "inclined plane"). It keeps sitting there until it is nudged, or the slope is gently struck, setting up vibrations. Then the block starts to slide. At that point it keeps sliding until it reaches the bottom. The block sitting at the bottom is stable. The block sitting on the slope but not moving is metastable. And the block as it is moving is unstable.
A real life example of this is an avalanche of snow. The avalanche is unstable (the snow is sliding down the mountainside). When the avalanche is over the snow is stable. Before the avalanche starts, the snow is metastable, since some small perturbation is enough to cause it to lose what might have seemed to be stability, but in fact was only metastability.