Simply put, Heisenberg's Uncertainty Principle states that it is impossible to know both the exact position and the exact velocity of an object at the same time. However, the effect is tiny and so is only noticeable on a subatomic scale.

The Heisenburg Uncertainty Principle is an equation that describes the uncertainty in measuring two variables in quantum mechanics. The beauty of it is that it can be derived from pure mathematics and the proof does not require the consideration of any real system. Many people get confused between the HUP and the Measurement problem. Put simply, the HUP is a quantitative assessment of uncertainty from maths, whilst the Measurement Problem is qualitative. The Measurement Problem is something like this- In order to study something you must interact with it, which causes a change. I explain it like this- say you want to see a car in the dark, so you shine a light on it. Obviously the light has very little effect, but if (in some strange parallel universe) you study the car by throwing bricks at it then this has a large effect. This is the measurement problem, when studying particles you shine light on them, bombard with electrons etc, this is akin to throwing bricks at a car. You results are therefore masked as you have had a big effect on the particle in order to study it. The HUP states that the product of the root-mean-square-uncertainties of two hermitian operators is greater than or equal to one half the modulus of the expectation value of their commutator. This sounds much more complicated than it actually is! As I have said this is derived from maths, and so requires very little knowledge of quantum mechanics, and the mathematics is not too difficult either (I can write the proof in one page). Unfortunately answerbag lacks mathematical notation so I can't easily provide the proof here.