You see, the human eyeball is basically a balloon, roughly spherical in shape. Like a balloon, it needs something inside it to fill it up so that it stays inflated. In our case, the filling that makes up the inside of the eyeball is the vitreous humor. This basically just means the "clear like glass jelly or fluid." This makes sense, in a way. it needs to be thick enough to keep the eyeball spherical, but also clear so light can pass through it to the retina, which is where the optic nerves connect to the proteins that detect light.
So, the little dots are usually called "floaters." These little guys are typically most visible against a really bright background, such as a clear sky, or a light bulb. They are probably made up of the proteins that make up the vitreous jelly. When they clump together, they can become visible, and it is likely that at least a few will be clumped and therefore visible in the right circumstances.
If you see tons of these guys at all times, regardless of the light level, it probably indicates that proteins are breaking off from the back of your eye at the retina, in which case you should go see a doctor. Itmight not be bad, but it can't be good.