IANAP, but my admittedly also very shallow understanding, is that when we're talking about the energy of the "vaccuum", we mean "energy associated with space itself".
A vaccuum is typically defined by the absence of matter in a volume of space (but not necessarily light or other energy). But let's exclude those too - there is no matter or electromagnetic radiation at all.
Even with those exclusions, at a fundamental level space appears to be a seething maelstrom of quantum particles popping in and out of existence. There seems to be some energy associated with "empty" space.
Some people posit that the vaccuum (i.e. space as we know it) may be "unstable" - that the particular energy it possesses could be lower than it is - and that we're just caught on a local bump in the energy landscape. If the vaccuum ever "fell off" that bump to a lower level, it would apparently spread at the speed of light across the entire universe from wherever it started, destroying everything that currently exists, and leaving behind... I don't know what. More vaccuum, but with a much lower energy associated with it, and with lots of new matter and energy created by the release of the vaccuum energy. Probably.
Anway, happy for a real physicist to correct me on some or all of the above - that's just my very lay understanding of what is meant by vaccuum energy.