the coat which I bought yesterday

Like the word "red" in the first example, the dependent clause "which I bought yesterday" in the second example modifies the noun "coat." Note that an adjective clause usually comes after what it modifies, while an adjective usually comes before.

In formal writing, an adjective clause begins with the relative pronouns "who(m)," "that," or "which." In informal writing or speech, you may leave out the relative pronoun when it is not the subject of the adjective clause, but you should usually include the relative pronoun in formal, academic writing:

informal

The books people read were mainly religious.

formal

The books that people read were mainly religious.

informal

Some firefighters never meet the people they save.

formal

Some firefighters never meet the people whom they save.

Here are some more examples of adjective clauses:

the meat which they ate was tainted

This clause modifies the noun "meat" and answers the question "which meat?".

They're talking about the movie which made him cry

This clause modifies the noun "movie" and answers the question "which movie?".

They are searching for the student who borrowed the book

The clause modifies the pronoun "student" and answers the question "which student?".

Did I tell you about the author whom I met?

The clause modifies the noun "author" and answers the question "which author?".

2. Restrictive & non restrictive clauses

Do the following pairs of sentences mean the same thing?

1a My uncle, who lives in London, is very rich.

2b My uncle who lives in London is very rich.