These are also known as self-certification mortgages or non-status mortgages. The creation of self-certification mortgages came about due to the large numbers of the self-employed experiencing great difficulty in obtaining standard mortgages. Although it's not impossible to get a standard mortgage, traditional lenders don't make it easy. Lenders tend to rely on payslips and P60's to determine your employment status but the self-employed can't provide these and so banks require at least 3 years of audited accounts proving the business' profitability.
This can be difficult depending on the length of time the business has been trading and the fact that most businesses don't necessarily see much in the way of profit in the first couple of years (and sometimes longer). Also, if the business owners take shares and dividends over a standard salary for tax purposes, their income can look pretty abysmal and they may seem like a bad risk for the lender.
Some mortgage lenders now offer self-certification mortgages where the applicant estimates their annual earnings instead of the lender relying on an employer or an accountant supporting their claim. As with other mortgage applications your credit history will be checked to appraise your ability to keep up repayments. Interest rates for self-certification mortgages can be slightly above average and the mortgage offer made to you will be based on you personal circumstances.