Volume is the amount of space a material occupies. It is a property whose value depends on how much material is present, which makes it extensive. A drop of water has a small volume; a lake of water has a much larger one. Same kind of stuff, very different values.
A region of space is a definite area or volume of the three-dimensional continuum in which all entities reside; it has to do with the size of something. Volume is how we put a number on that size. The value comes from a measurement procedure (a graduated cylinder, a displacement test, a calculation from dimensions) and that value is paired with a unit (liters, milliliters, cubic centimeters). Without the unit, the number is empty. To say a flask holds 250 is meaningless; to say it holds 250 milliliters is a measurement.
Volume sits among the core features of a phase, alongside mass, temperature, pressure, energy, and the others. Where mass answers how much material is present by weight, volume answers how much space that material occupies. The two answer related questions, and the relationship between them is interesting enough to have its own name: density. Mass divided by volume gives density, and the fact that the ratio behaves differently from either of its parts is what makes density a useful third property.
Like every extensive value, volume is conserved across partitions in the obvious way. Pour the water of a full pitcher into two glasses, and the volumes in the glasses sum to what was in the pitcher. The arithmetic is mundane and that is the point: extensive properties add up, which is exactly why they are the ones we count, total, and conserve.
Question
Why does pouring water from a pitcher into a glass change the volume of water in the glass but not the volume of water in the world?
Reveal Merrill's answer →Hide answer
Because volume is extensive. It tracks how much space the water in front of you takes up, and that depends on which water you are looking at. Pour some out and the volume in the glass goes up; the volume in the pitcher goes down by the same amount. The total volume of water present has not changed. Volume divides and adds with the sample, the way mass does, because both are answering "how much?"