The crossing of the Jordan River marks a profound turning point in the transfer of prophetic leadership. It is the exact moment the disciples of the prophets officially recognize a new leader stepping into the role of his master.
The primary approach among commentators is that the disciples directly witnessed Elisha splitting the waters of the Jordan and walking across. This miraculous act serves as undeniable proof of the profound spiritual and leadership transformation that has taken place within him. By watching the water divide, the disciples immediately understand that the spirit of Elijah has completely settled and come to rest upon Elisha [מצודת ציון]. He has received his master's power, allowing him to perform the exact same wonders [מלבי״ם, רלב״ג, ביאור שטיינזלץ].
Realizing that Elisha has now reached the same spiritual heights as Elijah, the disciples respond with deep honor. They bow down to the ground, an act that clearly shows their full acceptance of his new authority. They offer Elisha the very same reverence they previously gave to Elijah when he was alive and serving as the master of the prophets [רלב״ג, אברבנאל].