"Observation" means interaction with anything, which might be a sentient being or might simply be matter.
At very small scales (sub-atomic) particles can exist in several states at once. When they interact with anything else - even as small as another electron - they can experience "wavefunction collapse".
A "wavefunction" in quantum mechanics is the maths used to describe how something behaves (and that means everything, though there is no point trying to work out a wavefunction for say a bus, as it would be a) impossibly complex, and b) quantum effects are so unlikely and so minuscule at that scale as to be irrelevant, so physicists only talk about wavefunctions for tiny things, such as an electron).
The point of these wavefunctions is to describe the world in terms of probability - for instance, one cannot talk about an electron being in a particular place, but rather only of the probability of it being there.
(this is entirely different from the uncertainty principle. That states that certain complementary metrics cannot be known with complete accuracy at small scales. For instance, the more one knows about the momentum of an electron, the less one can know about its location, and vice versa. The effect is similar - you can't know what you want to know - but the underlying phenomena is different)
Wavefunctions can allow the superposition of several states - for instance a photon's wavefunction can allow it to be in two places at once, and even to interfere with itself.
However, if you try to to observe the photon being in two places at once, then the wavefunction "collapses", and the photon will appear in only a single place.
This has very real implications. In two slit defraction, a photon can go through two separate openings at once and then in effect "bump" into itself on the other side.
However, any attempt to try to watch it going through both slits at once will require something to interact with that photon, whether that be a human observer or simply the matter that makes up a piece of apparatus. That interaction causes the photon's wavefunction to collapse, and the quantum effect of the two slit defraction to cease.
(the uncertainty principle by contrast is the same whether or not the photon is observed)
It is interesting to apply this explanation to Schrodinger's Cat. The radioactive decay that is to trigger the release of cyanide and kill the cat can exist in two states only as long as it interacts with nothing else. There is no need for a human observer, and so no paradox - the wavefunction of the radioactive decay collapses when it interacts with the detector and the cat in the closed box, meaning that the cat is already either alive or dead when the box is opened.