Negative energy can refer to several different phenomena:
By definition, the potential energy between attracting bodies is negative, so that together with their kinetic energy, the total energy is zero. This is nothing magic, just a convention.
In quantum theory, there are several forms of energy which are negative, e.g. the Casimir effect and virtual negative-energy particles created along with normal particles for a short perdiod of time (as in Hawking radiation).
"Energy" cannot by itself be seen, but it can affect bodies and particles in a way that can be seen, as when the negative potential energy of an apple is converted to positive kinetic energy as it falls to the ground.
None of these energies have anything to do with dark energy, which is (perhaps, we don't know, really) more likely a form of energy behaving like a negative pressure, causing a repulsive force on space.