What do you mean with the statement A fixed supply means that real estate prices will fluctuate with demand?

The statement refers to basic microeconomics:

Under the condition of a fixed supply, demandalone determines price. Supply is constant.

Under other conditions, Supply is represented on a graph as a line that slopes upward, while demand is a line that sloped downward. That is that as the quantity suppliedincreases, so does price. As the price increases, the quantity demanded decreases. Where the two curves meet is called the Equalibrium.

Under the condition of a fixed supply, supply is not represented by a curve, but a vertical line. Demand is still a curve, but the quantity demandedcannot exceed the supply.

edit: That answer is hyper-technical, and reads like a modern textbook. The terms, "demand" and "fixed supply" refer exactly to this type of graph. In English, the question simply means that the price of real estate will go up or down depending solely on how much people are willing to pay.