One of the greatest and simplest tactics of raising suspense that any author has at his or her command is the raising of suspense by leaving a character in a potentially dangerous situation or a situation in which we wonder what that character will do next and move to a completely different character or scene, leaving us wondering what that character is thinking, doing and deciding. At a simple level, this is what is achieved in Book 15 when Homer delays the return home of Telemachus. We are left wondering what is happening to Odysseus and what plans he will be making. It also as well keeps us guessing about what will happen to Telemachus. Will he make it safely back to Ithaca? Will he have his long-awaited reunion with his father? Will they be able together to vanquish the suitors? Such questions keep us in suspense by this long focus on Telemachus and his journey home.
In Homer's Book XV of the epic The Odyssey, there are several reasons I would expect Telemachus' journey is delayed somewhat.
First, it heightens the suspense in the waiting that Telemachus has to go through to get home, just as we (and Odysseus) have begun to grow impatient with Odysseus' inordinately long return home. It is safe to assume that the delay is a good storytelling tactic.
It is also possible that Telemachus is being taught patience by the gods.
Additionally, it gives the audience a view of hosts who are welcoming and kind, as opposed to Polyphemus (the Cyclops) and Circe who were malicious. (Inhospitable behavior on the part of a host was frowned upon in Homer's time, and this was still the case in Shakespeare's time.)
Whereas Odysseus suffers from the dangers of wicked, malevolent "hosts," Telemachus endures the extreme opposite: hosts who are so gracious as to be insufferable, especially when the guest wants to or must leave, as with Telemachus's host Nestor. Though comic in one sense, Telemachus has been told his father will be returning home soon for vengeance against the suitors, and Odysseus's son is desperate to be there when his father arrives.