The air is full of microscopic particles - whether from pollution, brake dust, or just general dirt - which can become embedded in your car's paintwork. During the normal process of washing your car, these tiny particles are not always removed because they have too strong a purchase on the paint layer and are too small for your sponge or cloth to rub off.
To remove them you could use a polish, but polishes contain abrasives which actually remove a very thin layer of the paint surface. While this will get rid of any particles which are contaminating the paint, it will also remove part of the paint layer which protects your car. If you use polish too much, or if you use a polish which is too abrasive, you can actually damage the paintwork and leave your car vulnerable to corrosion.
The best way to remove small particles like these is to use clay bar in conjunction with a lubricant. Clay bar is a kind of polymer clay with mild abrasives in it. The clay uses the lubricant to hydroplane over the surface of your paint, so it doesn't actually affect the paint, but anything which sticks above the surface of the paint, such as particles of pollution, gets removed. The end result is an extremely smooth paint finish. Clay bar can only remove particles which stick above the surface of the paint, so it's no use on scratches or chips for which you will need polish, but if your paint is not actually damaged, then clay bar might be all you need to finish the 'cleaning' stage before you use a finishing product, such as a wax.
The effect of these microscopic contaminents builds up quite slowly, and is less noticable than other factors in the finish of your car, so a clay bar is not something you need to use very often. You can get products which can be used monthly, but once or twice a year is usually enough.
Clay bar should only be used after your car has been washed and dried properly, and it's best to move your car out of direct sunlight if possible.
The easiest way to get clay bar is as part of a kit with a spray bottle of lubricant. Spray the lubricant onto the car, and then rub the clay over it with a medium pressure - you shouldn't be scrubbing away. Only work on a small area of the car at a time, and make sure to keep the paintwork well lubricated.
You should be able to feel the difference between the areas you've clayed and those you haven't. Keep rubbing until there are no more bumps. Check frequently to see if the clay has picked up any hard particles and remove them. Also, you should occasionally knead the clay so that you're not always rubbing with the same bit of it.
If you drop the clay on the floor, throw it away. It will almost certainly have picked up grit and will damage your paint. Depending on the size of your clay bar, it might be an idea to cut it into smaller pieces, so that if you drop one of them you don't have to throw the entire bar away.