To gather (a head of) steam is to build up enough energy, strength, momentum, support, etc. to achieve a goal.
'The campaign really only began to gather steam in the late spring.'
'The movement toward unionization gradually gathered steam as workers began organizing.'
The expression comes from the way a steam engine works. Pressurized steam is the force which drives the engine. Until the steam is sufficiently pressurized it has no power to do this.
Sometimes people say 'to build up steam,' or 'to build up a head of steam.'
To gather steam is not the same as to gather speed. The definition you posted appears to be in error.
I hope this is helpful,
- For Teachers