What does this paragraph from the story mean?
"He was incredulous and then proud to find he could hold his breath without straining for two minutes.The words 'two minutes,' authorized by the clock, brought close the adventure that was so necessary to him."
In Doris Lessing's Through The Tunnel, Jerry is determined to swim through the long, underwater tunnel. He practices holding his breath but soon finds his nose bleeding due to his monumental efforts. Although dejected, he consents to rest for a day and is delighted to discover that his count has increased by ten the following day.
When his mother is not paying attention, Jerry times his breathing exercises by the clock in the villa. One day, he is ecstatic when he realizes that he has managed to hold his breath for all of two minutes. This is the quote you are referring to. The words 'authorized' refers to concrete proof (the clock's unmistakable pronouncement of time) of Jerry's accomplishment; this means that Jerry is that much closer to achieving his goal of swimming the tunnel. He is both 'incredulous' and 'proud' of his accomplishment. This just means that he can't believe he has finally succeeded in holding his breath for a specified amount of time (two minutes) without strain. He is justifiably proud of his achievement.
The quote refers to the instance when the adventure that is so necessary to Jerry is brought closer. Why is the adventure necessary to Jerry? It is to prove that he can, literally, swim with the big boys, that he has left his childish ways behind, and that he is ready to navigate new challenges and conflicts in life.