Experiment: you send electrons, one by one, from the source through the slits, to the detector. When I say one by one, I mean there is on average one electron in transit at a given time, so we can exclude some wierd interactions of electrons with themselves.
Outcome: interference pattern similiar to the one with the waves of water or light.
So, there is definitely something wavelike in the behaviour of the electron. In order to produce interference pattern it had to interact with himself otherwise, how can we explain it? So, we can think of it this way: electrons in transit to the detector do not travel with their definite position but they travel as a wave of many possible positions. This wave then comes to the slit and some part of the wave passes through one slit and the other part passes through the other, just like water wave would. And then they interfere.
I have given you an explanation for the observed phenomena. Now, about the observer...when it is said OBSERVER what is ment is some sort of interaction with the environment. So, in these cases, the observer is the detector put on one of the slits. This detector destroys the interference pattern, and again, we ask ourselves, how can we explain this? So we can think of it like this: When electron is not being detected, it is in many possible positions at the same time. But, when it is observed through detector which detects position, the elctron sudenly oicks up one of these possible positions.