Self-certification or 'self-cert' mortgages were perhaps too common before the credit crunch of 2007.
With these types of deal you simply stated how much you earned on your mortgage application without having to provide any proof. Provided the figures stacked up and your credit record checked out, you would often be offered a deal on that basis.
Some people chose this route because it was simply quicker and easier than going through the process of providing proof of income, but there was a rogue element where people simply lied about their income to borrow more than they could afford - which is a criminal offence.
These deals no longer exist, although where a borrower applies for a very low loan-to-value mortgage, say less than 50%, some lenders may 'fast track' their application.