What is the basic idea of loop quantum gravity? I have researched a little on loop quantum gravity (LQG), but all I got were very ambiguous explanations about loops and nodes that all end with mathematical equations.
If someone could give me a non-mathematical, clear idea of LQG, I would really appreciate it.
 A: Loop quantum gravity (LQG) is an attempt to unify general relativity and quantum mechanics. LQG attempts to treat gravity as a feature of spacetime as it is in general relativity, rather than as a force. The output of the theory is a picture of spacetime where space is granular (as a result of the quantization). Just as light can only be emitted in packets (quanta) space can only be traveled through by a minimum distance (in simpler terms, there is a minimum distance one can travel; you cannot travel an infinitely small distance). This minimum distance is the Planck length ($10^{-35}$ meters). 
Space is considered a very fine fabric, "woven" of tiny, finite loops that are only visible at the Planck length. The networks of loops that make up space are called spin networks, and the evolution of these networks over time is called spin foam. Spin networks represent the quantum state of the gravitational field. An image one can have is that every "node" in the spin network (a node is equivalent to a loop) is an elementary quantum of volume and every link between the nodes is a quantum area surrounding this volume. Spin networks quantitize quantum geometry, and spin foam does the same thing for spacetime. (There is more information about spin foam here and more information about spin networks here.)
Therefore, LQG predicts that space itself has an atomic structure. LQG is developing in two main directions: canonical LQG and covariant LQG, also known as spin foam theory. There are about 30 research groups worldwide working on both types of LQG. LQG has been applied to cosmology in what is known as loop quantum cosmology. This has applied LQG ideas to the early universe and the Big Bang, its most significant implication being that the evolution of the universe can be continued beyond the Big Bang in what is called a Big Bounce (you can learn more about loop quantum cosmology here). 
Let me know if there's anything specific you wanted to know about that I haven't addressed, though I think I've given a decent overview here. This website is very helpful and goes more in-depth into LQG.
Hope this helps!
