past-continuouspast-simplepast-tense
What's the difference between the past simple and the past continuous when using "from … to …"?
I read a book from 2 to 4pm.
I was reading a book from 2 to 4pm.
I built a ship from 2 to 4pm.
I was building a ship from 2 to 4pm.
I repaired my bike from 2 to 4pm.
I was repairing my bike from 2 to 4pm.
Past continuous is used for describing actions that take place over a period of time in the past - not at a moment. The definition you quote is misleading.
Thus we would say:
I was sitting
I was watching
I was eating
and so on, because all these actions take some time - and because we often use these statements to introduce something else that happened:
I was sitting on the fence when it collapsed
I was watching the cat when it caught a mouse
I was eating supper when she called.
We prefer simple past tense when we do not wish to emphasise the length of time they take - and for momentary actions:
I sat on the stool that I had made.
I watched the cat as it climbed a tree.
I ate supper before doing my homework.
In many of these cases you can choose between past simple and past continuous depending on the context and what you wish to emphasise. Both are acceptable.
So you could use any of the following combinations. All are correct. It depends on what you are trying to convey:
Daniel called you at one o'clock yesterday but you were here with me.
Daniel was looking for you at one o'clock yesterday but you were here with me.
Daniel looked for you yesterday while you were here talking to me.
For both example sentences, I agree with your book that "went" is correct and "was going" is incorrect. But why?
First, past continuous events aren't the main idea of the sentence. Rather, they provide the context for events in the simple past.
Second, if a simple past event happens "while" a past continuous event is happening, it always means the simple past event only happens after the past continuous event has started. 
In the first example sentence, with "was going", it would mean that you left your parents while you were going, as in, you left after you had already left. This is impossible.
In the second example sentence, if both clauses were in the past continuous, there would be no simple past story, so the sentence would be about nothing other than describing a scene, which might be the context for some other simple past clause. This sentence appears to be about what Meg did, so it should be in the simple past.
Best Answer
The difference is in whether you are choosing to present the activity as a completed whole, or as a process that continued. That is all.
There is no objective difference. There are no implications that are different.
There might be (but would not necessarily be) some different implications in what follows that statement. So if the next sentence after any of them was John came to talk to me, then with the "continuous" forms there is a suggestion that this happened during the activity, whereas with the simple past forms there is no such suggestion: it might have been during or after the activity. And even with the continuous forms, that suggestion could be overridden by something else in the discourse.