Derate. Engines are restricted to the max power output, stipulated within the AFM and agreed by the lessee/lessor to give greater engine life. Once done you can only operate to these power levels/speeds/weight restrictions.
Flexible Thrust. Say you have a ETOW of 77000kgs. You look at your airport performancd charts for your w/speed & direction, temperature, pressure/altitude etc and it shows you are okay for take off to 82000kgs (say speeds 154-162-164).
Flex thrust allows you to look down the charts finding what temp it would need to be for a max payload of 77000kgs (which is all you have) - say that's 50c - with speeds 152-157-159 - you can put this temp into A/C database as OAT and use these lower speeds. Saves engine life. Why use the higher speeds of 154-162-164 for a TOW of 82000kgs when you only need to lift 77000kgs.
There is more to it, but that's the basics.