Comic Strip provided by Dresden Codak 

 The position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision. There is a minimum for the product of the uncertainties of these two measurements. There is likewise a minimum for the product of the uncertainties of the energy and time.

The Heisenberg Uncertainty Principle 

   An odd aspect of Quantum Mechanics is contained in the Heisenberg Uncertainty Principle (HUP). The HUP can be stated in different ways; let me first talk in terms of momentum and position (it can also be thought of in terms of energy and time).

If there is a particle, such as an electron, moving through space, I can characterize its motion by telling you where it is (its position) and its velocity (more precisely, its momentum).

Classically, i.e., in our macroscopic world, I can measure these two quantities to infinite precision (more or less). There is really no question where something is and what its momentum is. Consequently, I can tell with infinite precision where that particle will at the next instant in time.

In the Quantum Mechanical world, the idea that we can know things exactly breaks down. More precisely, suppose a particle has momemtum p and a position x. In a Quantum Mechanical world, I would not be able simultaneously to measure both p and x precisely. There is an uncertainty associated with this pair of measurements, e.g., there is some dp and dx, which I can never get rid of even in a perfect experiment!!!.

Definition By University of Oregon 

How do this work? 

 Light can be considered as being made up of packets of energy called photons. To measure the position and velocity of any particle, you would first shine a light on it, then detect the reflection. On a macroscopic scale, the effect of photons on an object is insignificant. Unfortunately, on subatomic scales, the photons that hit the subatomic particle will cause it to move significantly, so although the position has been measured accurately, the velocity of the particle will have been altered. By learning the position, you have rendered any information you previously had on the velocity useless. In other words, the observer affects the observed.

Definition provided by H2G2 

     Important steps on the way to understanding the uncertainty principle are wave-particle duality and the DeBroglie hypothesis. As you proceed downward in size to atomic dimensions, it is no longer valid to consider a particle like a hard sphere, because the smaller the dimension, the more wave-like it becomes. It no longer makes sense to say that you have precisely determined both the position and momentum of such a particle. When you say that the electron acts as a wave, then the wave is the quantum mechanical wave function and it is therefore related to the probability of finding the electron at any point in space. A perfect Sine wave for the electron wave spreads that probability throughout all of space, and the "position" of the electron is completely uncertain.

Definition from Hyperphysics

A Word about Wave-Particle duality 

Typically wave-particle duality is as "wellllll it's when an electron behaves like a particle when it is observed, and behaves like a wave when it not observed".  The truth is don't think of as being a particle at one point and a wave at another, instead it's always a wave.  The Heisenberg uncertainty is about wave nature of the "particle" and it's a dimensional wave, a wave in position and a wave in momentum (think of as speed). The observation may reduce the size of the wave in position (fitting it to a small region, but not to a point) but the wave in velocity grows, this is what ramification of Heisenberg uncertainty.