What does leveling skills and how is it implemented? (Elex)

I propose here to open the discussion purpose abilities!
Example: melee Weapons - each new level increases the amount of damage inflicted by melee weapons.
What does the phrase leveling up, because it is mentioned in a larger number of abilities!
When you put the training points in this ability, what happens next?
With each new level of the hero (to infinity) will increase the damage of weapons, or means that damage is increased only once, in the three phases envisaged for this skill?
I DO NOT UNDERSTAND(((