It's for inheriting a plan from another ship. Saves having to do all the stage setups. It could be useful for example if you have a staged rocket and have the plan all set up for the stack to get into orbit and for the eject burn. But after you separate into an upper capsule you can grab the plan that is already set up from that stack.
To do it you click back to 1st stage the BCK (back) once more. You will see inherit from and either new or a ship name. You can click the ++ button to toggle through the possible choices. Only the ship in the same stage (location) as you are possible to be used for the inherit. Example if a ship has a plan and is still on Earth and you are in orbit, then you can't choose to inherit from that ship. But if it is launched into orbit then it becomes a candidate for the inherit.
Then finally to complete the inherit, click the EXE button.