Explanation:

Information Age: - in OA, the conventional dating of years, centuries etc is often replaced by a more generic techno-socio-political division into ages or eras. Just as today we speak of the bronze age, the iron age, the middle ages, the age of enlightenment, and so on, in the same way future history in this scenario is divided into periods like "Interplanetary Age", "Second Federation Era", and so on. The Information Age is the first of these periods, it corresponds to the twenty-first century of current convention)

Old Earth: - because OA is set many thousands of years in the future, when humanity and other sentient beings have spread among the stars, Earth is a distant memory to many; hence the term "Old Earth" is used.

AI: - Artificial Intelligence. These beings play a large role in OA. Some people today don't believe that AI is possible, and even argue philosophically or scientifically that AI is impossible. But see Ray Kurzweil, The Age of Spiritual Machines for refutations of those arguments.