Let's imagine I've got two brothers:
The next sentence doesn't contain enough information:
Defining clauses say who or what we are talking about:
Compare with extra information clauses:
But if you have only one brother you can say:
That can be used only in defining clauses:
But the following can be used in both types:
Whose can be used with both people and things:
Which can't be used with people in sentences such as the ones above, but it's common in questions:
And sentences like:
But this sentence is incorrect:
It's easy to make this mistake, but we have to use who here.
In defining clauses you can omit who, that, which etc. if the sentence still makes sense:
But this sentence doesn't make sense when you omit who:
The actual rule is that you can do it when the relative pronoun is the object of the clause - don't try to remember it.