That is simply a connector. It shows that a declarative clause forms part of a larger sentence.
- I understand. You are right. (two separate sentences)
- I understand that you are right. (The clause you are right has become the object of the verb in the larger sentence.)
That-clauses can have various functions in sentences. A that-clause can be the subject.
- That she should forget me so quickly was rather a shock.
It can be the complement.
- The main thing is that she is happy.
Many verbs can have that-clauses as objects.
- I will see that a meal is ready for you when you get home tonight.
- We knew that she would be happy.
Many nouns and adjectives can be followed by that-clauses as complements.
- His manners are so bad that nobody invites him to a party.
- You may go on condition that you will not come home alone.
Note that not all verbs, nouns or adjectives can be followed by that-clauses. For the structures that are possible after particular verbs, nouns and adjectives, see a good dictionary.
In many cases, it is used as a preparatory subject or object for a that-clause.
- She made it clear that she wanted to leave. (NOT She made that she wanted to leave.)
- It surprised me that she was still in bed. (More natural than That she was still in bed surprised me.)
The fact that
That-clauses cannot follow prepositions directly. We use the expression the fact that.
- The judge paid no attention to the fact that she had just lost her husband. (NOT The judge paid no attention to that she …)
- He held her responsible for the fact that she took food without paying for it. (NOT He held her responsible for that she took …)
- In spite of the fact that she had three small children he sent her to prison. (NOT In spite of that she had …