Non-defining relative clauses

The River Nile, which is over 6,500 kilometres long, is Egypt's main source of water.
This example contains information about the noun the River Nile.  The modern Olympic Games, which take place every four years, were first held in 1896.
This example contains information about the noun the modern Olympic Games

The are called non-defining or non-identifying relative clauses to avoid confusion with defining relative clauses.

The River Nile, which is over 6,500 kilometres long, is Egypt's main source of water.
It is clear which river - there is only one river Nile. The relative clause which is over 6,500 kilometres long gives extra information. The modern Olympic Games, which take place every four years, were first held in 1896.
It is clear which games - there is only one modern competition called the Olympic Games. The relative clause which take place every four years is extra information.
Unlike defining relative clauses, they do not tell us which person or thing as that is already clear.
Sentences with non-defining relative clauses are grammatical even if you remove the non-defining relative clause:
The River Nile, which is over 6,500 kilometres long, is Egypt's main source of water.The River Nile is Egypt's main source of water is a complete grammatical sentence. The modern Olympic Games, which take place every four years, were first held in 1896.
The modern Olympic Games were first held in 1896 is a complete grammatical sentence.

The relative clause usually comes immediately after the noun that it relates to. The Eiffel Tower, which was built in 1887, is not far from the Louvre museum.
The relative clause, which was built in 1887, relates to the Eiffel Tower. If you want to add a non-defining relative clause to the Louvre museum, it must go immediately after the word museum:
The Eiffel Tower is not far from the Louvre museum, which contains the famous portrait, the Mona Lisa
It is clear that it is the Louvre museum and not the Eiffel Tower that contains the Mona Lisa.

Relative clauses usually relate to a noun or noun phrase within the main clause. However, some non-defining relative clauses can relate to the whole of the main clause of the sentence. Compare the following examples: We had some ice-cream which was very unusual.
We had some ice-cream, which was very unusual. In the first example, the defining relative clause which was very unusual, relates only to the noun ice-cream - it was an unusual type of ice-cream. In the second example, the non-defining relative clause, which was very unusual, relates to the whole of the main clause: We had some ice-cream.
This time we are not saying the ice-cream was unusual. We are saying that it was unusual to have ice-cream - we do not usually eat ice-cream.

Non-defining relative clauses are separated from the rest of the sentence by commas.

Use which for objects (things). Do not use that in non-defining relative clauses.
The station, which was built in 1906, is due to be demolished.
Use who for people. Do not use that in non-defining relative clauses.
John Woo, who was born in China, has made a successful career in Hollywood.
Use whose for possessives.
The author, whose works have been translated into 50 languages, is working on a new novel.
Use where or preposition + which (formal) for places.
The family home in New Orleans, where Munroe spent much of his childhood, has recently been opened to the public.
The family home in New Orleans, in which Munroe spent much of his childhood, has recently been opened to the public.
Use when or preposition + which for times.
Christmas Day, when many people stay at home, is a quiet day in many western countries.
Christmas Day, on which many people stay at home, is a quiet day in many western countries.

The relative pronoun is never omitted with non-defining relative clauses.

The relative pronouns where and which are both used to talk about places. However, there are differences in the way that they are used. The old palace, where the royal family once lived, is now open to the public.
The royal family once lived in the old palace. He recently returned to St John's College, where he had studied as an undergraduate.
He had studied at St John's College. We can include the preposition at the end of the clause. This is common in spoken English.
The old palace, which the royal family once lived in, is now open to the public.
(This example is not very natural as non-defining relative clauses are not common in informal spoken English.) We can include the preposition before the relative pronoun. This is common in formal written English.
The old palace, in which the royal family once lived, is now open to the public.
When there is no preposition in the information contained in the relative clause, we use which, that, who etc. The main building, which was built in 1968, is currently being renovated.
We stayed at the Royal Hotel, which is conveniently located for the museums and shops.