What you have read in your textbook is equally true in English, too.
- 入学式は、このホールで行われます。
The entrance ceremony will be held in this hall (by us).
- 昔は、その考えが正しいと思われていた。
In the past, it was thought (by people) that the idea was correct.
The original (active) versions of these sentences are:
- このホールで入学式を行います。 (omitted subject = 我々 (we))
We will hold the entrance ceremony in this hall.
- 昔は、人々はその考えが正しいと思っていた。 (subject = 人々 (people))
In the past, people thought the idea was correct.
The book's explanation means you can omit the subject of the original (active) sentence once it has been turned to passive. See how "we (us)" and "people" can be omitted in the passive versions.
~(ら)れている is simply the combination of passive and ている (e.g., 今、私は見られている = "I am being seen now."; そのCDはもう発売されている = "The CD has already been released."). If you're not sure why you need ている in the second example, see the following questions.