You've interviewed several people and think you've finally narrowed down just the right one for the job. But don't make an offer just yet. References are personal contacts, typically former employers, colleagues and personal associates, that offer further insight into the applicant. If you want to know what the prospective employee is really like in a professional setting, or just make sure he's not Ted Kaczynski, former employers are one of the best ways to find out. If there are any potential problems, this is one of the best ways to find out - before you make an offer.
Some companies request references upfront, before the candidate has even interviewed.
But the most common practice is to narrow down your search to one or more of the best candidates and then contact their references. This effort is best spent as the final step in the hiring process, either to choose between equally qualified applicants or as the final check and balance for the applicant you've chosen. Most companies extend job offers with the condition that references check out. I have often felt, sir, that instead of our employers requiring references from us, we should require references from them. The applicant will provide you with a list of names and numbers.