In sum, this letter is about focus. Adding a slighter nuance to it, the lesson of this letter is about being present and in the moment. While Seneca applies this idea to reading, the key lesson is applicable in many aspects of our lives.
I think this is why it is important, as a young person, to read and learn from the classics. Teenagers and young adults need to stick with the classics and not be distracted by the latest fictional series. A young person needs to be brought up to speed, as it were, on history, philosophy and the sciences. If they spend enough time 'catching up' and focusing on what lessons we've learned as a civilization, then they will be in a position to add to the collective knowledge of a civilized society.
By sticking to these important texts, they can learn from them, and incorporate them into their personal lives. But if they 'get bored' with them, they risk the opportunity to change themselves for the better. Seneca uses a handful of analogies to make his point:
nothing hinders a cure so much as frequent change of medicine; no wound will heal when one salve is tried after another; a plant which is often moved can never grow strong.