Heisenberg was a pioneer of quantum mechanics, presenting a new picture of particles represented as vectors operated on by waves. The matrix formulation accounted for many of the properties of atoms.
Much more intimately connected with the name of Heisenberg though is the uncertinty principle. The principle implies there is a limit to the possible accuracy of any measurement. This limit is a fundamental matter and not due to any experimental design flaw, and cannot be overcome. More precisely, certain physical quantities are paired, so that the value of each quantity separately cannot be simultaneously be determined with complete accuracy.
Energy and time are paired quantities. If the uncertainties in the value of energy and time are
respectively then
Position and momentum are paired quantities. If the uncertainties in the value of position and momentum are
and
respectively then
The implications of the uncertainty principle are profound. A deterministic Universe allows us to predict the future with certainty in principle. All we had to do was determine the position, direction, mass and speed of each particle at a particular known and the future could be calculated according to the principles of mechanics. Because however, the simultaneous measurements of position and momentum (and velocity) can not be done to arbitrary accuracy, accurate predictions are impossible beyond a certain time. We may be able to predict with confidence an hour hence, but not a day. Predicting the future of the Universe in this way is much like predicting the weather. You can typically rely on a one day weather forecast and even believe the forecast when predicts rain at 3 o clock, but the weather next week is another matter – the weather can diverge wilder from what is expected, due only to the limitations with which we can measure current conditions.