This is complex. When people are referring to runout, they’re generally talking about how much the tip of the tool moves. This is caused by a lot of things, as @WillAdams says, the collet can be off center (poorly made, dirt in it or the nut), but it just keeps going up the chain - the bearings/bushings in the spindle, flexibility in the tool while it’s chattering, I’m sure there are others. Don’t confuse this with backlash, which is inaccuracy in the mechanical movement of the mill due to spacing in the mechanics such that the machine can actually move. That’s a different creature.
How to account for runout in your design isn’t totally straightforward, and depends on exactly what is causing it. If you’re running, say .002" of runout (you have to measure it), any cut by that tool is going to essentially be .002" over the nominal size of the end mill. So you adjust the size of the tool to match. The problem with that is that the runout at the tip of the tool is usually larger than the runout at the top of the tool, and that means measuring both and creating a fairly complicated “tool” in your CAM software. If the runout is not always stable (ie. sometimes it’s .005" and sometimes it’s .001" measured at the same part of the tool - it wobbles) then you have a whole lot of problems.
How important all this is depends on what you’re trying to do. I generally ignore it, and instead focus on preventing chatter, which seems to have a bigger impact on my part quality.