Elijah the prophet follows God's command completely and retreats to a hidden location. His departure unfolds in two distinct stages, representing two different layers of his actions [מלבי״ם].
The first layer is spiritual and hidden. By simply leaving his home and detaching himself from his usual surroundings, Elijah sets a profound spiritual process into motion. This act of separation influences God's providence, causing Him to hold back the rain in the heavens and bring the decree of drought into reality.
The second layer is entirely physical and visible. This involves Elijah's practical journey to the brook, where he physically settles down and remains in a state of complete isolation [ביאור שטיינזלץ].