Compare these two sentences.

The students who were late were expelled. (defining)
The students, who were late, were expelled. (non-defining)

In the first sentence we mean that only those students were expelled who were late for class. This means that there were other students who were punctual and they could stay. The second sentence expresses that all the students were late and all of them were expelled.

In mathematical terms this means the following. The defining relative clauseA group of related words containing a subject and a verb. defines a subset of a given set and makes a stateA condition that exists at a particular time. E.g.: I am sick. This melon weighs two kilos. ment on the elements of the subset. The non-defining relative clause makes a statement on all the elements of a given set.

Diagrams

Non-defining relative clause
The difference between defining and non-defining relative clauses Relative pronouns