I get this error message somewhat frequently, but I have no idea what it means. Would anyone happen to know what generally causes this to pop up?

Simple: you create a variable supposed to hold an object, but omit to initialize it. When you call a method on it or try to access one of its fields, you get a NullPointerException. Which is funny, now that I think of it because AFAIK nowhere else in Java they talk about pointers.
Variables of type object are actually just a reference to an object. If they are declared at class level (or global level in Processing), they are initialized by default at null, ie. pointing nowhere.

Some common cases:

PVector v; // Missing v = new PVector();
v.x = 3;

PGraphics g; // Missing g = createGraphics();
g.beginDraw();

PImage i = loadImage("non existing");
image(img...);

int[] ar; // Missing ar = new int[20];
ar[0] = 1;

PVector[] va = new PVector[10];
va[0].x = 1; // Missing va[0] = new PVector();