One use of the word that is as a complementizer, a part of speech that is a type of subordinating conjunction in traditional grammars. Complementizers introduce complement clauses, which are sentential clauses that may or may not stand alone and are the argument of the main verb:
- I believe that she is a good person.
- It seems that he can perform miracles.
In other words, the clause she is a good person (which stands alone as a valid sentence), is the argument of the verb believe. The argument of this use of believe is a complement clause, and so may optionally be introduced by the complementizer that.
When that is used as a complementizer, it is optional. Omitting or including the that complementizer is a stylistic decision. Here is a good article that can help elucidate the factors that go into the decision (also available as a podcast at the same link).