We use that as a conjunction to link a verb, adjective or noun with the following clause.
Verb + that-clause
Verbs commonly followed by that include reporting verbs (say, tell, admit, etc.) and mental process verbs (believe, think, know, hope, etc.):
They said that four million workers stayed at home to protest against the tax.
The survey indicated that 28 per cent would prefer to buy a house through a building society than through a bank.
He knew that something bad had happened.
Do you think that they forgot to pay or that they stole it?
Adjective + that-clause
We use be + adjective + that-clause to express opinions and feelings. Some adjectives commonly used in this way are sure, certain, right, important, afraid, pleased, sorry, surprised, worried. We can omit that with no change in meaning:
It’s important (that) we look at the problem in more detail.
I’m sure (that) you’ll know a lot of people there.
They were afraid (that) we were going to be late.
Noun + that-clause
We use a noun + that-clause to express opinions and feelings, often about certainty and possibility. We also use that with reporting nouns. Some nouns commonly used in this way are belief, fact, hope, idea, possibility, suggestion, statement, claim, comment, argument:
He is also having intensive treatment in the hope that he will be able to train on Friday.
Dutch police are investigating the possibility that a bomb was planted on the jet.