That

That can serve different functions in English. I will discuss four uses.

Pronoun
As a pronoun, that usually refers to something specific.

What kind of car is that?

That can be used to refer to an event.

The bicycle race finish was very close. That was really exciting.

That can be used to refer to something farther away in contrast to this.

That calculator is mine; this one is hers.

Relative Pronoun

That can be used to form two kinds of clauses: noun clause and adjective clauses.

Noun Clause:

That he was wrong is very clear now.
The important thing is that she did not panic.

Adjective Clause:

The store that used to be on this corner was my favorite place to buy magazines.
Storm is the name that her mother gave her.

Conjunction

With some adjectives and verbs, that can serve as a subordinate conjunction.

He is sorry that he missed her performance.
I wish that she would pay closer attention.
She knew that she should wait longer.

so that

I worked hard all afternoon so that I could pay my rent this month.

Adjective

That is used to point at a specific thing.

That rose is my favorite one.
He brought that guitar to the party.

Leaving out that

In some cases, that can be left out.

So that clauses

She baked a cake so that her sister would have something special for her birthday.
She baked a cake so her sister would have something special for her birthday.

That can be left out of clauses when it is the object of the clause.

She went to the store that sold the best watches. (that is the subject so it can not be left out.)
She went to the store that her sister told her about. (that is the object – her sister told her about that store- so it can be left out)
She went to the store her sister told her about.