As said, the Quantum Realm introduced in Ant-Man is one of the most important discoveries (if we can call it this way) presented in the MCU after Tony Stark developed the arc reactor. If the latter is a powerful source of energy which can power a rather heavy Iron Man suit for a long period of time, we don't really know too much about the former. Or do we?
Thankfully, after seeing Ant-Man and how the Microverse was adapted for the MCU, we can say that we have a pretty good idea as to what the Quantum Realm actually is. Check it out "“ but you may want to look the other way, because here be spoilers!
The Quantum Realm "“ in the comics

In the comics, the Quantum Realm (which is a rather sophisticated and scientifically acceptable way of adapting the comic book name) is the Microverse, which is an alternate dimension. However, in itself, it isn't tiny, being as big as any other universe (if we may say so "“ it is comics, after all). However, the gateway between these dimensions is a small one.
In this way, the MCU's Quantum Realm cannot be reached by a person, unless that person makes itself really small.
There are some theories (already) which say that Ant-man doesn't actually shrink, because this would be physically (and thus, scientifically "“ and the MCU is, thus far, scientific-based) impossible. Instead, the Pym Particles continuously transport the user between dimensions. It is just a theory about a theory from the comics "“ so it may as well work out this way.
In the comics, the Microverse has its own origin story, being created by a time traveler, after a savage war from the future. In the MCU, Ant-Man has barely touched this new dimension, so we don't actually know how it came into existence. However, we do know something else about it.
Check out on the next page how the Microverse was adapted!

