After the first medical studies performed on cigarettes found a definitive link to lung cancer, cigarette companies responded in different ways, including adding a filter to their products. The public found comfort in hearing that a 'safety feature' had been added to a harmful substance and so the sales of filter-tip cigarettes were very successful, just as they are today.
But what do these filters do? It's clearly evident that people are still being harmed by cigarettes today, even though every drag they inhale passes through one.
The purpose of the filter is to take out some of the nicotine and tar from the smoke before it is inhaled. Some "light" cigarettes take it a step further. These have holes punctured in surface of the filter so air can mix in with the smoke before being inhaled. This means the smoker reduces the amount of smoke going into their body during a drag, meaning less nicotine is taken in overall.
Really this is just a clever marketing scheme. The body of a smoker builds up a nicotine level that needs to be maintained or adverse affects occur; if a smoker needs to have x amount of nicotine in their system and the filter rids some of it from a cigarette, then the person will just need to soon smoke again because he or she didn't get the proper dosage from the one cigarette. In the end, the cigarette companies win because the user ends up buying more of their product.