If you were not born in the UK, the process of applying for British Citizenship is known as Naturalization. You will be able eligible for naturalization as a British citizen one year after acquiring Indefinite leave to remain in the UK(PR). You shouldn’t have any serious criminal or immigration records during your stay in the UK. You should also meet the additional requirements to be eligible including the total number of absences, language requirements, life in the UK test, etc.
British Citizenship by Birth
Every child born in the UK are not considered as British nationals. You may be eligible to apply for a British paspport if either of the parents are settled in the UK and the child is born in the UK.
Whereas children born outside UK and with parents settled status in the UK will need to register for the citizenship.
Use the following links for more details.