While it is raining- Clause

When the book says 'while it is raining' is a clause, it actually means 'it is raining' is a clause, without 'while'.

We can't start while it is raining.

Means:

We can't start during the time it is raining.

Just as you can't say 'during the time it is raining' is a clause, neither can you say 'while it is raining' is a clause.

While it is raining is really a clause with the subject it and the predicate is raining. While is a conjunction here, so it cannot be the subject. It only connects the main clause (we can't start) with the subordinate clause (it is raining).

Here are more examples of sentences with time clauses (time clauses are used to indicate the time when an event in the main clause takes place) (the subject of the sub-clause is in bold):

1. As soon as you arrive, give me a call.
2. I read it while you were drying your hair.
3. I went there when I was a child.