You may have seen the play/film Copenhagen, about Neils Bohr and Werner Heisenberg. The play mostly investigates the idea of psychological uncertainty; not only do memories claim different 'facts', but even the attitudes and memories of the persons involved change with each retelling. This is compared to the uncertainty principle of QM, in which the momentum (closely related to the speed something is moving) and the position of a particle cannot be exactly specified. While this is a good film, the definition of uncertainty leans more toward the English language use of it (not able to know something for certain) rather than the mathematical definition.
According to the theory of QM, electrons are best described by wave functions. For waves on a pond, the medium being "waved" is water. For sound, it is air. For electrons, it is probability density. Particles are described by waves "superimposed" on top of each other, with the peaks and valleys of some waves sometimes adding and sometimes canceling each other out. The direct result of this method of describing matter is the precise mathematical relationship:
∆x∆p≥ℏ/2which reads: "the uncertainty in position, times the uncertainty in momemntum is greater than or equal to h-bar over two" While this is a strange and important result, it doesn't mean that we have reached a limit of understanding; rather, we have seen that the universe behaves in this predictable way which includes a fixed uncertainty.
You may have seen this talk by Rob Bell from "Everything is Spiritual", in which I believe this idea of uncertainty is taken a bit too far:
While it is interesting to compare our understanding of God to his creation, it is dangerous to say that there is something about the physical world that it so mysterious that "all [scientists] can come up with" is something they cannot "conquer or put in a box". You see, scientists are not trying to conquer anything. They are trying to describe and understand the wonders of the natural world. It is fun to draw parallels between God and the forces and energies of nature, but we must be cautious of saying we have found something only explicable by God. What will happen when this "gap" is filled in by some deeper theory? Let's not lose our sense of wonder, but let's not get overzealous with our theology.
Schrodinger, trying to understand and explain this idea of adding or "superimposing" wave functions and how this relates to the uncertainty principle, came up with his famous cat-in-a-box illustration:
Of course, this is just an illustration and wouldn't actually work in real life, but it does explain a little bit about how weird this understanding of matter really is. Isn't it wonderful that our world is so complex and surprising?