Many drugs lose their effectiveness if you keep taking them. A person is becoming tolerant to a drug when they have to take more of it or take the same dose more frequently, to get the same effect as they got at first. For example, if you take a decongestant for a cold over several days, the effective time becomes shorter and shorter. Similarly, if you take opiate medications to control pain, you may need to take more to achieve the same level of pain control. In such a case, developing tolerance does not mean that you are addicted to the drug.
For more information, check out Above the Influence.