what is metastable system?

Metastability is a general scientific concept which describes state of delicate equilibrium. A system is in a metastable state when it is in equilibrium (not changing with time) but is susceptible to fall into lower-energy states with only slight interaction. It is analogous to being balanced precisely at the top of a round hill, rather than safely at the bottom of a valley.

To understand metastability supersaturated solutions take following example:

In air that is supersaturated with water, water droplets may precipitate upon being disturbed.Thus a change of state of a supersaturated solution can take place on slight changing of conditions of temperature,pressure and volume.