There is no precise biblical answer to this question, but we can offer some ideas. First of all, when God made Adam and Eve they were sinless and, basically, physically perfect. When sin entered the world there was an obviously harmful effect upon their bodies; they died. Genetically speaking, when they were first made their health was so good that their natural inclination was to live a long time. But since sin is in the world and it has an effect on people (we get sick, grow old, and die), some have said that genetic mutations (which occur with the birth of every new person) are passed down from parent to child. With each passing generation, new genetic problems are introduced and an accumulation of them over many generations has contributed to our shortened life spans.
Another theory is that before the flood there was a canopy of water vapor encompassing the whole world. Some theologians think there was no direct sunlight on Earth, and that instead the sun's rays were refracted through this water vapor canopy and a diffused light passed through the clouds and lit the world. This refraction produced plenty of light for our planet, but as the theory goes, it also filtered out some harmful cosmic rays that contributed to us dying sooner than we should. In the flood of Noah's time, the Bible says that the floodgates of the sky were opened (Gen. 7:11). This implies that a great amount of rain fell; hence, the idea of a canopy of water vapor suspended in the sky. After the flood the canopy disappeared and the full brunt of cosmic rays fell upon the earth, so people's life spans were shortened. At least, this is how the theory goes.
Finally, in Genesis 6:3 God says, "My spirit shall not always strive with man, for that he also is flesh: yet his days shall be a hundred and twenty years." It might be possible that God shortened the lifespan of man because of man's great wickedness. After all, the flood came soon after this statement of God. It is also possible that the 120 years was prophetic... that's how many years were left until the flood was to occur.
So, though we don't know exactly why the people of the Old Testament lived so long, we can offer some good explanations.