Physicist: Physicists are among the laziest and most attractive people in the world, and as such don’t like to spend too much time doing real work. In an effort to streamline equations “natural units” are used. The idea behind natural units is to minimize the number of physical constants that you need to keep track of.
For example, Newton’s law of universal gravitation says that the gravitational force between two objects with masses m1 and m2, that are separated by a distance r, is , where G is the “gravitational constant“. G can be expressed as a lot of different numbers depending on the units used. For example, in terms of meters, kilograms, and seconds: .
In terms of miles, pounds, and years: .
In terms of furlongs, femptograms, and fortnights: .
Point is, by changing the units you change the value of G (this has no impact on the physics, just the units of measurement). So, why not choose units so that G=1, and then ignore it? The Planck units are set up so that G (the gravitational constant), c (the speed of light), (the reduced Planck constant), and kB (Boltzmann constant) are all equal to 1. So for example, “E=mc2” becomes “E=m” (again, this doesn’t change things any more than, say, switching between miles and kilometers does).
The “Planck length” is the unit of length in Planck units, and it’s meters. Which is small. I don’t even have a remotely useful way of describing how small that is. Think of anything at all: that’s way, way, way bigger. A hydrogen atom is about 10 trillion trillion Planck lengths across (which, in the pantheon of worldly facts, ranks among the most useless).
Physicists primarily use the Planck length to talk about things that are ridiculously tiny. Specifically; too tiny to matter. By the time you get to (anywhere near) the Planck length it stops making much sense to talk about the difference between two points in any reasonable situation. Basically, because of the uncertainty principle, there’s no useful (physically relevant) difference between the positions of things separated by small enough distances, and the Planck length certainly qualifies. Nothing fundamentally changes at the Planck scale, and there’s nothing special about the physics there, it’s just that there’s no point trying to deal with things that small. Part of why nobody bothers is that the smallest particle, the electron, is about 1020 times larger (that’s the difference between a single hair and a large galaxy). Rather than being a specific scale, The Planck scale is just an easy to remember line-in-the-sand (the words “Planck length” are easier to remember than a number).
That all said (and what was said is: don’t worry about the Planck constant because it’s not important), there are some places on the bleeding edge of physics where the Planck length (or distances of approximately that size) do show up. In particular, it shows up in the “Generalized Uncertainty Principle” (GUP) where it’s inserted basically as a patch to make physics work in some fairly obscure situations (quantum gravity and whatnot). The GUP implies that at a small enough scale it is literally impossible, in all situations, to make a smaller-scale measurement. In the right light this makes it look like maybe spacetime is discrete and comes in “smallest units”, and maybe the universe is like the image on a computer screen (made up of pixels).
How bleeding edge is the GUP? So bleeding edge that there isn’t even a wikipedia article about it. Like a lot of things in string theory (this is an opinion), these sort of patches may prove to be mistakes. So, spacetime may come in discrete chunks, but the most we can say is that those chunks (if they exist) are very, very, very, very small.
You’d never notice (at least, the experiments designed to notice haven’t so far).