Adaptability actually makes STAB moves do 2x damage instead of 1.5x damage, making them the same as a single-type super effective attack. In case you don't know, STAB means Same Type Attack Bonus. This means that a move that is used by the user that is the same type (i.e. Flareon using Flamethrower) is powered up by 1.5 times or an extra 50% damage is dealt than normal.
Adapt, in the dictionary, says "to make suitable to requirements or conditions; adjust or modify fittingly."
So what this means is that the Pokémon is "adapting" to the fact it did a STAB move and making it more suitable by increasing the damage dealt.