We call it also 'indirect speech' and it is used to talk about different points in time in the past. When we use some verbal tenses in direct speech, the tense changes in reported speech in some cases:
There are some structures that do not change in reported speech:
agree: She agreed to do my homeowork.
offer: She offered to bake some cookies for us.
refuse: She refused to tell us her secret.
demand: She demanded to be told the truth.
threaten: She threatened to punish us with more work.
promise: She promised to visit her grandparents.
claim: She claimed to have done all the paperwork.
advise: They advised me to come to the meeting.
allow: They allowed us not to be present.
beg: She begged him to stop screaming.
command: He commanded them to put down their guns.
encourage: Mary encouraged him to keep working hard.
forbid: He forbade you to take those pills.
invite: The boy invited her to come to his party.
want: The doctor wanted her to go to rehab.
instruct: She instructed the kids to do the handicrafts.
permit: My mom permitted me to eat more candy.
urge: He urged the people to go out quickly.
order: My friend ordered me to help him with his job.
remind: My teacher reminded me to do the project.
warn: She warned us not to forget the date.
admit (to): He admitted (to) sending the letter.
accuse of: He accused me of stealing his money.
apologize for: Mary apologized for being late.
complain to... of...: She complained to the company of not sending the package.
deny: The students denied pushing the button.
insist on: My parents insisted on me wearing warm clothes.
suggest: They suggested going to the cinema.
complain: He complained that the children were too loud.
deny: She denied that she had stolen the money.
explain: John explained that he was going to a funeral.
exclaim / remark: They remarked that the baby was crying.
promise: Victoria promised that she would visit us.
boast: The girl boasted that she had brilliant marks.
inform: We informed them that they had been accepted.
claim: The government claimed that the president had the answer.
agree: The students agreed that the exam was pretty difficult.
suggest: I suggested that the children had to study harder.
explain to someone: He explained to me how to solve the activities.
wonder + question word + clause: She wondered how she could pass the test.
wonder + question word + infinitive: She wondered how to pass the test.
wonder + if / whether + infinitive: The boy wondered whether to study or not.
Reported Speech Rules (British Council)
Reported Speech Statements (British Council)
Reported Speech Questions (British Council)
Daisy's Summer Job (Listening, British Council)
Reported Speech Activities (Pefect English Grammar)