such that often begins a definition.

In the sentence you cited, you could replace such that with having the quality.

A rule...having the quality there is a unique element in the second set assigned to each element in the first set

Here is another use of such that.

John's test anxiety was such that it affected his performance.

So the anxiety affected his performance. If the anxiety had been different it would not have affected his performance, but the anxiety was such that, of a kind that, or a degree of anxiety that affected his performance.

Such that is often used in math. Here it is in a GMAT question.

x and y are positive integers such that x=8y+12...

So x and y are positive integers having the quality x=8y+12.