The map is not the territory metaphorically illustrates the differences between belief and reality. The phrase was coined by Alfred Korzybski. Our perception of the world is being generated by our brain and can be considered as a 'map' of reality written in neural patterns. Reality exists outside our mind but we can construct models of this 'territory' based on what we glimpse through our senses.

The metaphor is useful for illustrating several ideas in a more intuitive way:

Scribbling on the map does not change the territory: If you change what you believe about an object, that is a change in the pattern of neurons in your brain. The real object will not change because of this edit. Granted you could act on the world to bring about changes to it but you can't do that by simply believing it to be a different way. For example, you could send a ball to the other side of a field by kicking it but you cannot send the ball across the field by believing it is on the other side of the field (unless you are connected to a machine that scans your brain an kicks the ball when you believe it's on the other side, but let's not be pedantic). The strategy that normally gives most control over reality is one where the 'map' is aligned to match the 'territory' as closely as possible. This way you can create accurate models and predict what will happen as a consequence of your actions. eg: If you know where the ball is, and you know what will happen if you kick it, and you want it on the other side of the field you can decide to kick it to achieve the desired end state of ball being across the field. Wishing the ball across the field would be futile. For some strange reasons (but explainable at least in principle, nothing is strange if you truly understand it), humans are wired to sometimes let their beliefs slip into what they would like to believe instead of what the evidence suggests. That is like erasing a mountain off a map because you would like to pass there or drawing an oasis on the map in a desert because you would like some water.
The map is a separate object from the territory and the map exists as an object inside the territory: The analogy encourages us to look from a frame of reference other than from the inside outward and hopefully realize that not only do we cause things to happen, and things cause other things to happen, but also things have caused us to be the way we are. For example, Why is the sky so blue and beautiful? It must have been made like that just for me. It was made beautiful so that I would enjoy looking at it. Except it's the other way around. The sky was not made to fit our sense of beauty, the sky was here before us, we have a sense of beauty that evolved to fit the sky because the sky happened to be blue! In a sense the sky caused us to be what we are (creatures who mostly agree that a blue sky is beautiful).

See also

Mind projection fallacy
Map and territory