Dust particles are tiny bits of rock, ash, and organic matter that have been ground into fine pieces by the wind and wear. Although these particles are more dense than the air that surrounds them, they have trouble falling through the air because as soon as they move faster than about a snail's pace, they experience considerable air resistance or drag forces. A dust particle has trouble falling through the air because the upward drag force it experiences while descending even a few millimeters per second is enough to balance its weight so that it stops accelerating downward. Because dust particles have so much trouble descending through air, they tend to be swept along with moving air. That's why areas of your home that have large air currents tend to accumulate relatively little dust--the dust is swept along with the air currents and doesn't have time to descend all the way to the floor or furniture. But in areas of your home with fairly still air, the dust can slowly settle out so that it coats all the surfaces.
Dust is everywhere, either settled on a surface or swirling about in the air. Every time you open a door or window, the dust in your house "refreshes" -- new dust is ushered in and old dust is stirred up from its resting places to swirl about the house again. You may be surprised to know that things like aerosol cans also contirbute to dust, since they contain microscopic solid particles. And then there's the gross stuff: hair, sloughed off skin, etc. Pets can be a big source of "dust" by both shedding and by tracking it in when you whistle for dinner. And if you live in a dry climate, the air there may contain more stuff than in more humid environs (ever see the air around Denver in the summer? Blech!).
Some types of air purifiers help reduce the dust in your house, but sadly nothing will make it go away completely, so don't throw out those feather dusters!