In AskiaSurf, inheritance is the process through which questions and response matchings are carried across successive waves, without the need for you to continually perform manual intervention whenever you add a new wave.
When adding a volume to a wave, you specify whether or not to use inheritance (see add new volume dialog for further details). Volumes can inherit only from volumes in the previous wave. You can select any volume from the previous wave. If inheritance is used for a wave, the wave is said to inherit the question and response matchings from the previous wave.
For example, suppose wave 1 contains the question Q3 - Airlines and wave 2 contains the same question, but with a different response list (new airlines have been added). Let's assume that you matched these two questions together when you added wave 2. However, in wave 3, if you inherit from wave 2, this matching is already taken into account, so you will not need to make this matching manually again (nor for any other previously matched questions). If you do not inherit from wave 2, then AskiaSurf will flag the questions up an imperfectly matched, and you will have to check the matching again.
Inheritance thus saves you a great deal of time when adding new waves.