Imagine I am holding a tennis ball, and I tell you to close your eyes until I hide it. I then tell you to look for it, to "detect" it. Mathematically it could be in any given location, and there are odds for any of those locations. The odds in some areas are less likely than in others.
The idea of an electron "being" somewhere is a bit misunderstood in that we tend to think in in terms of the particle being a hard physical object like a marble or a golf ball that is in a specific place, a hard physical object in a well defined and set location.
Quantum mechanics deals in probabilities, remember that the objects we are talking about are NOT hard physical balls or marbles, and the very act of detecting them affects them.
A better way to think of it is to try to picture the location of waves in the water. I am not talking about the classic surging tidal wave that you surf on, but small ripples on a pond when you throw a little pebble into it. The concentric rings of ripples that move outward.
Particles seem to move somewhat like that and settle into frequencies to form atoms of different types. Now the important thing, the waves do not have any set specific start or end points, they just gradually ease up out from the water at no specific point, and where they do so fluctuates.
Remember that these are all just simple and arcane analogies, simply to give you a bit of a "feel" for it. In any case, that is what they are talking about when they say that a particle is "everywhere". In order to calculate the position of a particle what you are doing is dealing with the probabilities of finding it within a certain location (where does the wave begin or end). Since it's never in a specific well defined place, and since where it is can fluctuate, and since the very act of detecting it can affect it (and change it), all you can really do is calculate probabilities. There is a mathematical probability of it being "everywhere", that is to say, every location in the universe has a mathematical probability of it containing some part of it that is not exactly zero.
There are pictures of exactly this sort of rippling on the web, i'll post a couple of them for you below