Depending on many factors, a space may tend to damp certain ranges of frequencies, and other frequencies may resonate, due to the shape, dimensions, and acoustic reflectivity of surfaces. The placement of the sound source plays a role in this. If you produce sound wave that change in frequency, from low to high, (a "sweep"), at a consistent power level, and measure the resulting sound at any point, you will find that spaces will tend to have an uneven response throughout the range of frequencies. These bumps, ("nodes") in the response will have peaks that will occur near notes of a scale that the person is describing as the "rooms note". This is caused in part by reflections, or absorption of the signal, and these effects are dependent in part on the wavelength of the signal. If you encounter this, and find it detracts from the sound you are looking for, you could use EQ, or some type of notch filter to try to counter the effect. If the room conditions change, (say, by people entering, or leaving the space), the response may change. I would not be too concerned about how an empty room sounds, but if you find that a particular performance space sounds much worse than most, you may want to try something to reduce the effect. If you are having a problem with a recording space, you should make the effort to find a solution to room resonance problems. So, room dimensions, shape, surfaces, and contents will all affect the response. Room resonances are not necessarily bad. Think of how a pipe organ sounds in a cathedral. The same instrument would sound very different outside, or in your living room.
Hopefully someone here who is trained, and more experienced in these matters will be able to add to my non-expert explanation.