An odd aspect of Quantum Mechanics is contained in the Heisenberg Uncertainty Principle (HUP). The HUP can be stated in different ways, one of these ways is in terms of momentum and position.
If there is a particle, such as an electron, moving through space, you can characterize its motion by telling where it is (its position) and what its velocity is (more precisely, its momentum). Now, you can say something strange about what happens when you try to measure its position and momentum.
The preceding is a statement of The Heisenberg Uncertainty Principle. So, for example, if you measure x exactly, the uncertainty in p, dp must be infinite in order to keep the product constant.
This uncertainty leads to many strange things. For example, in a Quantum Mechanical world, you cannot predict where a particle will be with 100 % certainty. You can only speak in terms of probabilities. For example, you can say that an atom will be at some location with a 99 % probability, but there will be a 1 % probability it will be somewhere else (in fact, there will be a small but finite probabilty that it will be found across the Universe). This is strange.
We do not know if this indeterminism is actually the way the Universe works because the theory of Quantum Mechanics is probably incomplete. That is, we do not know if the Universe actually behaves in a probabilistic manner (there are many possible paths a particle can follow and the observed path is chosen probabilistically) or if the Universe is deterministic in the sense that I can predict the path a particle will follow with 100 % certainty.
A consequence of the Qunatum Mechanical nature of the world, is that particles can appear in places where they have no right to be (from an ordinary, common sense [classical] point of view)!
This notion has interesting consequences for nuclear fusion in stars.