The definition appears to be different throughout the world, in the UK it is:

Most mountains are classified using two factors:

1. the height of the summit above sea level - in the UK mountains must be over 610m (approx 2000ft) to be called 'mountains', and
2. the amount of re-ascent required on all sides from a neighbouring mountain to reach that summit - usually 30m (approx 100ft) or 150m (approx 500ft) depending on the system adopted.