What conditions do we need to see dust particles in the air?
A bright narrow beam of light in a dark room
Dust particles are always present in the air. Normally, they reflect less light, because the particles are very small. They can only be seen when a strong beam of light passes through the air. This is called Tyndall Effect. A very strong concentrated light beam reflects off of the dust in the air which can be seen in a darkened room, which is normally not seen.
Our eyes become more sensitive to light in dark rooms, especially if we give them a few minutes to adjust. Also, the illuminated dust in a beam of light shows up because of the contrast between it and the dark background when the room is dark.