Can someone tell me if there is a definition for energy. I don't mean a type of energy such as kinetic or potential etc. We talk about empty space having energy but what is it? Thanks
You need to look at vacuum energy from the perspective of Quantum Field Theory. In QFT and related theories, particles are simply excitations of underlying fields. These fields have quantized energy values and, as all quantum systems, have a ground state with a finite amount of energy.
One could say that the claim "remove all of what exists in space" to be impossible since particles and fields are effectively two forms of the same thing.