I hesitated responding because this is going to be a bit handwaving, and I'm not sure that I'll do it right. But given that nobody else took this up, here we go.
In (perturbative) quantum field theory, an interaction between two particles is calculated as a sum of contributions, which can be depicted as different interaction schemes. These terms can be calculated easily using formalised drawings known as Feynman graphs. When things (calculations) go right, then the "simplest" interaction schemes are also the most important ones. That means for instance, that you get "most of the answer" by just considering simple, elementary interactions. But, there are small "corrections" due to more complicated interaction schemes.
Let us consider an electron that collides with an electron. The "simplest" interaction scheme is: the incoming electron sends out a virtual photon and that one gets accepted by the target electron. This is the most elementary "electron interacts through electromagnetism with target electron". Just this single interaction scheme gives you, in most cases, already a good part of the final result.
But there are more complicated interaction schemes. For instance, the target electron sends out a virtual photon, that virtual photon splits into an electron-positron pair, then recombines back into a virtual photon which is finally absorbed by the target electron, and the incoming electron sends out a virtual photon which is absorbed by, say, the virtual positron in the created (and annihilated) pair. That's (a priori) a small contribution, but it is there, and it does change the final result a bit.
If you insist on saying that the incoming electron interacts through a simple electromagnetic interaction with the "target" as in the first contribution, then you can picture the second contribution as a kind of "cloud of virtual pairs" swarming around the initial target electron.
Now, as these interactions are always there when there is an electron, you cannot separate the "bare electron" from these extra contributions. Even in complicated interactions, there will always be these extra contributions, so it seems as if a "real electron" is a "bare electron" together with a "cloud of virtual electron-positron pairs" around it. The higher the energy of the incoming particle, the more "obvious" will be this cloud. That's vacuum polarisation.
So it is a way of wanting to think into elementary interactions while in fact the interaction scheme is more complicated.
). The main manifestation of vacuum polarization is that the effective charge of the electron seems to change (increase) when you go to higher collision energies. That can be visualized by saying that you "penetrate deeper in the polarisation cloud and see more of the bare charge that was partially shielded by the polarization".
