vacuum expectation value

Ordinarily we think of empty space as having nothing in it — pump out all the air and particles and you get a perfect void. But for the Higgs field, the lowest-energy 'empty' state is not nothing: the field sits at a definite, nonzero level everywhere, even in the deepest vacuum. That standing background value, the level the field holds in completely empty space, is its vacuum expectation value, usually shortened to VEV. It is like the still water level in a flooded valley: not a wave, not an event, just the constant baseline that is always there.

Quantitatively, the Higgs VEV is the place on the rim of the Mexican-hat potential where the field comes to rest, and its measured size is about 246 GeV (a unit of energy used as a stand-in for the field's value in particle physics). This single number sets the scale of mass for everything that gets mass from the Higgs. The mass of any particle is its VEV multiplied by how strongly that particle couples to the Higgs field: a strong coupling times 246 gives a heavy particle, a tiny coupling gives a light one. The W and Z boson masses, and the electron and quark masses, are all this VEV times their individual coupling strengths. If the VEV were zero, every one of those particles would be massless.

The VEV is the concrete number behind the slogan 'the Higgs field is switched on.' It marks the scale of electroweak symmetry breaking — roughly the energy at which, running the early universe backward, the Higgs field would melt back to zero and the symmetry would be restored. A useful caution: the value 246 GeV and the various coupling strengths are inputs measured from experiment, not things the Standard Model predicts from first principles, and why the VEV sits at exactly that scale (rather than vastly higher) is the open hierarchy problem.