1/ A vacuum is a medium in which the pressure is much lower than atmospheric pressure. In this sense a vacuum is not the absence of matter but merely a depletion (e.g. interstellar space, a vacuum chamber). Note that a region of space with a perfect vacuum (no particles) would still contain fields caused by particles located outside the region. It would therefore not really be a "vacuum" in the usual sense of the term.
2/ In quantum theory it refers to fields of minimum energy state in which there are no real particles. This is an absence of matter, but it is not "nothingness", since this "vacuum" state does have special properties. In a simplified way it can be seen to be populated with virtual particles (as opposed to real particles) that cannot materialise spontaneously but that can disturb the propagation of real particles.
The theories actually predict the existence of several distinct vacuum states. The transitions between these various vacuums play an important role in physics in several phenomena (spontaneous symmetry violation, quantum chromodynamics, instantons etc.).