Relative clauses are used to add information to the noun or pronoun they modify. Sometimes this clause is essential to the entire sentence. If you are without a relative clause, the sentence may not make any sense.
For example: "A person who was a former criminal will not be a potential candidate for a job at the police office."
If you erase the clause, the sentence above will not make any sense: we are not certain as to what kind of person is eligible for a job at the police office. These are called "defining relative clauses".
Now if you have a relative clause which provides interesting information, but isn't essential to the sentence in terms of meaning, you can still use the sentence without the clause as we will understand what the sentence is elaborating about.
E.g.: The knight, who is clad in ebony armour, lunges forth against the ferocious beast.
These are called "non-defining relative clauses"; you'll easily recognise them by punctuation.
Warning: Use who, whom, whose, or that for defining relative clauses; with the exception of that, use the first three relative pronouns for non-defining clauses.