Quantum foam
A quantum mechanical concept that emerged in 1955 was the spacetime foam, or the quantum foam. This idea was devised by John Archibald Wheeler, who was an American who revived the interest in general relativity after WWII. Niels Bohr, along with Wheeler, put forth ideas about nuclear fission. Also, the objects that were predicted in the early 20th century that underwent gravitational collapse, Wheeler associated with the term; "black hole." Wheeler also coined the term: quantum foam. He also coined the term: wormhole.
Wheeler proposed that, because of quantum mechanics, (the Heisenberg uncertainty principle), given sufficiently short intervals of time and distance, spacetime's very geometry will vibrate. This would be different from how we observe the smoothness of space on macroscopic scales. These would be large fluctuations in this spacetime. This would give space a foamy character.
John Wheeler
A complete theory of quantum gravity would be able to describe space at very microscopic scales. There is no real reason that space at these scales, has to be smooth. Space could consist of very small, not definite and changing components of spacetime. Space at this scale could flux in a foam manner.
There is no reason space must be smooth.
Planck length
1.616229(38)×10−35 meters. <- Planck length
This is a base unit in the Planck units of measurement. This system was developed by Max Planck, who was influential in the development of quantum mechanics for his theory of black body radiation, which was sufficient to understanding higher frequency and lower wavelengths of thermal radiation. However, this thermal radiation was set into equilibrium with harmonic oscillators in the way it realized its energy, which was, quantized. These were discrete bits of energy. Planck decided a significant constant for the constant of proportionality. This was his famous Planck's constant, and, this gave way to our current understanding and measurement of the Planck units. These are based on Planck's hypothesis that nature consists of discrete units. There is a theoretical significance.
There is a general conception that the Planck length is the smallest possible unit of length. This is technically not a convention in physics. This would actually violate Lorentz symmetry. However, the strings, of string theory are modeled to be on the scale of the Planck length.
Theories of quantum gravity, should take place on the Planck length. This is the scale at which the effects of quantum gravity are believed to become significant. Each time a black hole swallows one bit of information, the surface area of its event horizon grows by one Planck area.