Before you begin: to understand how to use adjective clauses, you have to know how to use Passives, so do the lesson on Passives before you do this lesson on reduced adjective clauses.
What's a reduced adjective clause?
He hit a dog running across the road.
running across the road
the reduced clause describes "dog"
The ones made in Taiwan are better.
made in Taiwan
the reduced clause describes "ones"
Please notice how a reduced adjective clause usually works just like an ordinary adjective clause - it follows the noun it describes. In the two examples above, first we have the noun ("dog", "ones") and then we have the reduced clause that describes it.
Why is it called "reduced"?
This type of clause is called reduced because it is a reduction of a full adjective clause.
Full adjective clause
He hit a dog which was running across the street.
Reduced adjective clause
He hit a dog running across the street.
There are two differences:
The reduced clause doesn't have a relative pronoun (it doesn't have "which").
The reduced clause doesn't have a verb; it has a participle - in the example above, the participle is "running".