"Karma" means "activity", and the law of karma is the law that regulates the reactions to our activities. The law of karma is the natural law of action and reaction. In physics this is expressed by Newton's law, "For every action there is an equal and opposite reaction". Or, in Christian theology, "As ye sow so ye shall ye reap".
From a practical point of view this means that good actions give good results and bad or destructive actions give bad or less fortunate results.
It should be noted here that all souls are essentially good. This means that just because someone gets a bad reaction it does not mean that they are a bad person. Another important point is that karma is temporary. This means that although we may be experiencing a particular set of circumstances right now those circumstances will change in the future. This could happen in this life or even future lives. Not only is karma temporary it is also possible to change one's karma, or even get rid of it altogether by acting spiritually in the service of God.
Good reactions include things like wealth, beauty, intelligence and happiness. Bad reactions include things like poverty and disease. In order to fully understand how karma works the concept of reincarnation must also be looked into. See the page on Reincarnation for more information.
Karma (good or bad) creates a continuous cycle by which one is entangled in repeated actions and subsequent reactions. As long as one is in this cycle one will naturally experience both happiness and distress. The philosophy of the devotees of Krishna teaches how to break this cycle and achieve a state of eternal happiness known as liberation in a pure relationship with Krishna (God).
From the spiritual point of view, that of eternity, it doesn't really matter if one has "good" or "bad" karma. This is because past material karma does not impede one from making spiritual advancement.