Any clause set off by commas is non-restrictive. Non-restrictive means that it you remove it, it does not change the meaning of the main clause.
1) There are a lot of charities which need good advice.
If you remove "which need good advice", the sentence doesn't really have any meaning. Therefore, it is restrictive. It restricts the meaning of "There are a lot of charities" to those which need good advice. [that or which can be used in a restrictive clause]
2) The horse, which she bought last year, is six years old.
If you remove the bit between commas, you still have a meaningful sentence:
The horse is six years old.
3) My bike, which has a broken seat, is in the garage.
If you remove "which has a broken seat" you still have a meaningful sentence.
My bike in the garage.
That only occurs in restrictive clauses and can sometimes be left out:
- The cars that I saw on the street were black.
- The cars I saw on the street were black.
- All the cars that were broken down on the street were black.
About which and that:
Restrictive relative clauses are typically [bolding and italicising mine] introduced by that, as well
as by whose, who, or whom. Note that in British English, the word
which is often used interchangeably with the restrictive that:
✓ She held out the hand which was hurt.
This common British construction is not strictly incorrect in American English, but it is generally avoided, especially in formal
Oxford Dictionaries on which and that