The short answer is diffusion.
According to kinetic molecular theory, all particles of all substances are in constant motion as long as the temperature is above absolute zero.
In solids, the motion is mainly the internal vibration of atoms of the substance, but in liquids and gases the individual particles can move about.
You can see this in a liquid if you place a tea bag on top of a container of water. Over time the tea diffuses into the water and the entire container becomes tea. The rate at which this takes place depends on the temperature with diffusion occurring faster as the temperature increases.
In the case of the perfume, perfume is very volatile. This means it easily changes from a liquid to a gas at room temperature. When you spray the perfume, tiny droplets of the liquid are atomized into the air where they quickly evaporate. The gas particles move randomly about, diffusing into surrounding air in the room, becoming more dilute as they spread out. Soon the entire room contains some of the perfume molecules.
Of course this is also true for the odor of a skunk, rotten eggs, and leaking natural gas.