That is also a subordinate conjunction that can be used to start noun clauses and relative clauses.
That he likes me is not important
Where That he likes me is the noun clause, performing the function of subject.
The things that they taught me are useless
Where That they taught me is the relative clause describing "the things", maybe what confused you here was the fact that To teach is a ditransitive verb, which is a verb that carries two objects:
I taught him a lot of things
Where him is the second object (a.k.a indirect object) and a lot of things is the first object (a.k.a direct object)
In the example you used (The things that they taught me at school) That is serving as the direct object of the verb Taught if we turn it into a phrase, we get:
They taught me the things at school
They taught the things to me at school.
You could also replace that for which
The things which they taught me at school.