I think I most likely heard this metaphor from Jordan Peterson, the clinical psychologist and Internet sensation, in a video in which he was telling a class a story about a little dragon living in a house where a family also lived. The dragon grew bigger and bigger, yet the only person that seemed to see it was the little boy of the family, while his parents relentlessly refused to acknowledge its existence. Finally it grew so large it filled the whole house so that when it got up and moved around the house moved around as well.
While this is a cute little story (about ignoring important issues I think?), there's something else Jordan mentioned. He said something about the dragon being either behind you or in front of you.
So, say that each of us have our own dragon living inside our heads - that burden we need to bear, different from individual to individual - and we know we must somehow deal with the dragon, or else it will spit fire out of its mouth and make us roast.
The question is, is the dragon chasing you or standing in front of you? Is it preventing you from taking a break and catching your breath from all the running, or is it stopping you from going forward, requiring you to slay it in order to proceed?
This is a very interesting analogy. You might think intuitively that since the dragon, in essence, emerges from your subconscious, from your Resistance, it would be easier to think of it as something you must kill in order to gain power over and move forward - after all, you yourself are your worst enemy.
But this way, absolutely nothing is stopping you from staying still for the rest of your life.
While with the other option - the dragon is chasing you - you can go in any direction you want, but you have to keep going without stop. You cannot stand still. You must be progressing constantly. Or else the dragon catches you.
It sounds somewhat agonising, the thought of not being able to rest, ever. But of the two options, it's the only one that guarantees success.