To understand this, you have (unfortunately) to completely abandon the idea, that the electron is orbiting the nucleus. You have to accept, that you cannot really track the motion in every detail (not because of measurement, but because of nature).
I will try to give you a short and full explanation without too many details but I have to introduce a weird concept (in the classical sense).
One of the main results of "quantum mechanics", the theory of really small stuff (which was a revolution 100 years ago), is the so called "uncertainty principle". You can best think of this in the sense of a photograph. Take two pictures of a moving person:
- One time you get a crisp picture of the person. You know really well where the person is located but you cannot say something about the velocity (maybe a bit).
- The second time it is blurred. You just can say, that the person is somewhere around this blurring but not exactly where. On the other side you may be able to track the velocity of the person by the blurring effect.
This is just a methaphor, but it at least explaines this uncertainty principle in some sense. The crucial point: uncertainty in position and velocity are linked! If one of them goes up, the other one goes down.
Now the electron
If it would fall into the nucleus, it would be exactly located at the position of the nucleus. This would raise the uncertainty in velocity, therefore the kinetic energy ($T=mv^2/2$) and it would "escape" from the nucleus again (it may sound odd, but perfect knowledge of position would mean an infinite uncertainty in velocity!). Of course, such a situation is prevented (by the same mechanism) before the electron hits the nucleus.
What is the electron doing?
One principle in quantum physics is, that particles like to go into a state, where they have the smallest amount of energy. By increasing the uncertainty in the position (blurr), the velocity uncertainty goes down, thus the kinetic energy will decrease. Therefore it desires the most uncertainty in position. The only thing preventing the electron to be a free particle is the attraction by the nucleus. It so to say limits the maximum uncertainty in position.
Now you see, why we cannot speak of classical orbits anymore: because of uncertainty in both, position and velocity, we have to accept, that we just can track the electron down to a "cloud" around the nucleus with some speed.
I hope this explanation was clear in some sense. It has the price, to abandon things like orbits and to accept things like the uncertainty principle. But despite quantum mechanics beeing an overall "weird" theory (philosophically) at all, it explaines lots of things in our modern world and is considered to be the right theory for these applications.