After securing the spear and water jug from Saul's camp, David carefully retreats and repositions himself to address his pursuers from a place of safety. He moves across to the opposite side of the valley [ביאור שטיינזלץ], with some suggesting he actually navigates across a body of water to reach his destination [מצודת דוד]. He then positions himself at the top of a mountain, a high vantage point that allows his voice to carry across the distance and reach Saul's camp.
This specific choice of a high and remote location is driven by a real fear for his life. David wants to ensure he can escape safely in case Saul's men wake up and attempt to chase him down [מצודת דוד, רלב״ג, אברבנאל]. The vast space between the two locations establishes a massive physical gap. Sometimes, climbing a tall mountain involves a long and winding path, yet the actual straight-line distance to the bottom remains quite short. To avoid this vulnerability, David makes sure that he does not merely take a long escape route, but actually creates a large, undeniable physical distance between himself and the camp [מלבי״ם].