In Naruto, Bleach, One Piece, Reborn, and possibly many others, there are timeskips. Why are these so prevalent?
There can be many reasons, but I personally think that the most important one is to give an opportunity for the characters and the story to develop to a new phase.
Naruto is a perfect example for it. What did we have in the first part? We learned about the main characters of the series, got acquainted with them, got familiar with their personal stories. We also learned about who were the true antogonists of the series. With that knowledge, we came to the time-skip.
But what was the situation before the time skip? All of the main characters were too weak to really be able to compete with the antogonists. What if Pain (spoiler)
came to destroy Konoha in the end of the first season? What would happen?
The anime would probably have ended just there, that's what. By including a time leap, the characters are given the opportunity to change, gain new abilities and powers. A lot of background events might have happened. After the time skip the series are almost reborn: while the readers/watchers already know the personalities of the main characters well, they once again have no idea of their abilities and powers, no idea about the current situation in the world. It opens a lot of opportunities for the story developing. It's also so easy to use, and to correct mistakes with. If you see there's a mismatch somewhere in the story, you can always explain it by the events that happened during the time leap! Very convenient, isn't it?