That answer is unclear, and even sounds incorrect.
The fact is that in quantum mechanics we only know the mathematics, and the results of experiments. Quantum mechanics is one of the most solid theories we have, and it has made plenty of predictions we have later proved to be correct, over and over. We don't understand the underlying "logic" behind those weird effects, however. There are multiple "interpretations" that are offered to explain that quantum behaviour.
In the Copenhagen interpretation, for example, there is indeed a change of behaviour when you observe a quantum particle: it goes from wavelike behaviour to particle-like behaviour -- the so-called "wave function collapse". And contrary to what a lot of people struggling to understand quantum mechanics think, this wave function collapse is NOT caused by physical interaction with the measurement instrument. It is the mere fact of recording the state that causes this collapse. The measurement does NOT "bump" into the particle, or something like that, causing it to change behaviour by purely classical means. In any case, the Copenhagen interpretation is arguably scientifically untenable -- or at least incomplete, as it doesn't explain why the wavefunction collapse really happens. And it even involves a "fudge factor" whereby you ignore what the math is suggesting to you (see the video I recommend at the end of this answer, to fully understand what I mean here)
Another interpretation is the many worlds interpretation. It suggests that all possible outcomes of a wave function actually happen in a multitude of superpositioned "universes". When you observe the path taken by the electron, for example, you (and everything else that is already entangled with you -- possibly the entire universe?) enter an entangled state with that particle, and as a result the wavefunction applies to you AND the particle. In other words, you are simultaneously in all possible states of observing the particle in every single one of all of it's possible paths. That's why each you that is part of any one of those specific entangled states, is aware of only one outcome out of all of the possibilities: hence the particle-like behaviour you now observe.
There are a few other interpretations. But mathematically speaking what happens is that the observer enters an entangled state with the observed particle. As a result the whole "complex" of both the observer and the observed is in the superposition (or wave-like) state. This sounds a lot like the many-worlds interpretation, although it doesn't necessarily suggest that the latter is what the physical universe behaves like...
I recommend the YouTube video: "The Quantum Conspiracy: What Popularizers of QM Don't Want You to Know" (a Google Tech Talk). It explains all those things much better than I can.