"Such a thing" means "a thing like that". It's mostly used in two totally different situations. One is in sentences like the one at top. Another example:

How could you do such a thing?

This is a sentence that you say when someone does something horrible to you.

The other situation where "such a thing" is used is in the expression "There is such a thing as ___":

Is there such a thing as love at first sight?

This means "Does love at first sight exist?" or "Is it real?"

The negative version of this is "there's no such thing". Notice that it doesn't include "a" before "thing":

I remember being really disappointed when I found out there was no such thing as Santa Claus.