You might be able to understand better what "one" stands for if you replace it with "you". In many languages, when talking about a hypothetical person, "you" is used in colloquial speech.
For example, if Person A says to Person B,
This situation makes you think, doesn't it?
This sentence doesn't mean that the situation made Person B think. It means that it would make anyone think.
Since this "you" can often lead to situations where the addressee of the utterance says, "Are you talking about me? No, this doesn't apply to me", — "one" is used instead.
One could say these problems would make her rethink her approach to life.
It means simply "It could be said that..."
His response makes one wonder whether he understood the question at all.
This means that X's response probably makes anyone wonder. The speaker is definitely wondering, but s/he doesn't want to restrict the conversation to him/herself and makes the sentence apply to some abstract "anyone". It is a way to remove discussion from the speaker or the addressee so as to make it more impersonal (and not use "me" or "you").
Grammatically speaking, this word is a deictic. It is a placeholder for something else.
Regarding this particular sentence, it seems to be an ad hoc coinage (so not really an idiom that would be repeated by other speakers of English) based on constructions (much more widespread) such as:
something sent someone into a fit of rage/laughter/coughing etc.
This construction is used mostly for situations or actions that qualify as an outburst (similarly to how, if you kick a ball, it will send it into the air). Someone could try to use it metaphorically to imply that a transition from one state to another was very sudden; that a certain action was initiated very suddenly. But these metaphors often don't sound right, including this situation—because thoughts, while they can pop up in your mind, are not usually described in terms of outbursts.