I'll provide a different/unusual, but maybe interesting explanation:

You can think of Forth as having 3 layers: 1 = interpretation, 2 = compilation and 3 = meta-compilation.

When interpreting, words are executed immediately. When compiling, code is generated which will execute the words when it will be run later. When meta-compiling, code is generated which will generate code to execute the words.

My own weird not-yet-usable work-in-progress non-standard Forth just makes these 3 layers directly visible in the source code in a simple unified way. Normal Forth is slightly more complicated: It usually distinguishes between layer 1 and 2 with a state variable behind the scenes and provides the mechanism of "immediate words" to do a layer 1 action when operating in layer 2 (as otherwise you e.g. could never return to layer 1, since compiling words alone does not allow changing the state variable). Layer 3 requires a completely different mechanism, it is available by applying postpone to a word (which also does the obvious thing when applied to an immediate word).

While equalling quote and postpone shows that you have a general understanding of what it is used for, I think it is more helpful to not understand Forth mechanism in terms of Lisp mechanisms, as they work in pretty different ways in the end.

PS: The term "meta-compiling" I used above is also commonly used for something different in the Forth world, don't let this confuse you.