If you run against a wall you can predict with 100% accuracy that you'll end up with a headache; the probability you can pass through the wall is quite low...but what if you are an electron?
This is a bit more complicated because it is difficult to say WHERE you are in the first place!
The only thing you can say is that there is a certain probability, say 60%, that you are at a certain position. This is because you, as an electron, are now a wave-particle entity that Quantum Physics describes only from the point of view of probabilities.
Now, you are an electron running against a barrier (a potential barrier, such as a wall charged negatively that for the electron is the same as a brick wall for a person) and you do not pass (you are reflected back) because again the probability to find you beyond the barrier is very small (say 0.0000000000000000001%)...but now you can call in other billions of billions of electrons and all run against the wall....Quantum Physics then evaluates the probability of finding one electron beyond the barrier...and finds one of them!!!!!
Basically, Quantum Mechanical entities are dominated by probability and, being very small, can operate in huge numbers so that even filmsy probabilities in our big world become quite acceptable microscopically!