Certain physical properties exist in pairs: position and momentum, energy and time, and others. No matter how accurate the measurements, both qualities cannot be known accurately (on the atomic level; in everyday life objects are enough greater than the possible error to make it negligeable, but in quantum physics it becomes critical). Since the measurements depend at the very least on the interaction of a photon with the particle under observation, they can get no more accurate than the wavelength of the photon used to observe. As the wavelength of the photon decreases, however, the momentum increases, meaning that when the photon interacts with the particle both will change momentum, thus messing with the observed phenomena.
It is impossible to know both where a particle is and at what velocity it is traveling with enough accuracy to predict its actions very far into the future, or to reconstruct its behavior very far into the past. This ignorance, according to Heisenberg, was the inevitable result of observation: thus the famous quantum principle that the act of observation changes both observer and observed.