In your example sentence, we have a case where English is more context dependent than Japanese. We usually see it the other way around such as in a sentence like
りんごをたべた。
The reader fills in the "who" of the matter: whether it's "I" or "you" or someone else.
But, in a situation like:
Wash the white and blue dishes. The red ones are fine.
both languages are leaving out the part which says,
You don't have to wash the red dishes.
Some people will parse the following
白と青の皿を洗って。赤いのはいいから。
as
Wash the white and blue dish. Because the red one's a fine, [you don't have to wash them.]
But for me, that doesn't help you to see why the Japanese insists on putting から there. It doesn't help you understand when you yourself should be adding such a から at the end of your sentence. The above snippet just provides a way for seeing how to make sense of the sentence after the fact of hearing. In a way it misrepresents Japanese as omitting something when, in fact, in English exactly the same thing is being omitted. In this case, it's English that's being more context dependent here than Japanese because English is not announcing, as the Japanese is, that an explanation has just been provided.
Just about any time something functions as an explanation in Japanese, it will be followed by から or の. To my way of seeing, it's better to view the dialogue as having a different portion omitted.
Wash the white and blue dishes. [Why only the white and blue dishes? Because] the red one's are fine.
In this case, you can clearly see how it's English that is omitting something: the "because".
This approach doesn't work for every such instance of a trailing から or の. For example, if someone is pestering you to do something and you're getting tired of being pestered, the following would work fine in Japanese...
もういいんだよ
It's a bit more idiomatic and such expressions are easy to pick up on a case by case basis.
But for the sort of examples I'm referring to, find some Ted talks in Japanese. You'll hear plenty of からです and んです. The speaker's providing an explanation for what they've just said in a manner where in English we'd just have the blunt sentence and leave it to the listener to gather that it's an explanation.
