The law requires an independent person to sign off that a firm's financial statements are "true and fair" and have been prepared using the relevant legislation...
Updated August 2018
The law requires that an independent entity certify that a company's accounts represent a "true and fair" view of its financial condition, and that the accounts have been prepared using the relevant legislation (in the UK, that's the Companies Act). The firms that carry out this work are auditors.
These are typically firms of qualified chartered accountants, who spend time at the company, talking to managers and checking records. The auditor is looking for fraud, or large errors in either the numbers that make up the accounts, or the narrative that appears in, say, the accompanying director's report.
Auditing in the UK is dominated by the "Big Four" accountants:PwC, KPMG, EY and Deloitte. Between them, these companies audit more than 95% of the UK's top 350 listed companies.
In theory, auditors are meant to be working on behalf of a firm's shareholders rather than its management after all, the shareholders are the ones who need to know that the accounts are trustworthy. However, in practice auditors are hired by executives rather than directly by shareholders, and the lack of competition in the sector has led to concerns that relationships between companies and their auditors can grow too cosy over time.
This is far from the only concern. Auditors make the majority of their money by selling unrelated services to the very companies that they audit, which suggests plenty of scope for conflicts of interest.
The sector came under even greater scrutiny in after the high-profile failure of government outsourcer Carillion, which was given a clean bill of health by KPMG just before it issued a huge profit warning.