Answer by Brian Bi:
The answer is actually very simple. Unfortunately, a lot of pop science writers want to make it seem more mysterious and profound than it actually is, so they don't bother to explain it properly.
Think for a moment: what does it mean to observe or measure a system? It means the system is allowed to interact with the measuring apparatus. Based on the consequences of this interaction on the measuring apparatus, some information regarding the system can be deduced.
For a simple example, consider measuring the temperature of a system. If you insert a thermometer into a glass of hot liquid, the alcohol in the thermometer will expand. The reason it does so is that the energetic molecules in the liquid transfer energy into the thermometer.
But if you hold the thermometer far away from the liquid, its reading won't change, because the molecules in the liquid are prevented from interacting with the molecules in the thermometer. Thus, no measurement is occurring. The system must be allowed to exert some influence on the measurement apparatus, if measurement is to take place.
As we know, interactions in nature are fundamentally reciprocal. Newton expressed this as his Third Law of Motion: for every action there is an equal and opposite reaction. If a molecule in the system collides with a molecule in the measurement apparatus, and the latter gains momentum, the same precise amount of momentum is lost by the former. Even in quantum mechanics, where the notion of force is abandoned, conservation of energy and momentum continue to hold.
When we observe a system, the system acts on the measurement apparatus, and the measurement apparatus acts on the system. As you observe, so shall you disturb.  That is why the system's behaviour is changed by observation.
 I have seen this called the Heisenberg uncertainty principle before. Do note that this is inaccurate; the Heisenberg uncertainty principle fundamentally has nothing to do with observation or measurement.