Definition
The IRS form a freelancer, contractor, landlord, or investor hands to whoever will pay them, not to the IRS. It supplies your legal name, address, and taxpayer identification number (a Social Security number or an employer identification number) and certifies that you are not subject to backup withholding, so the payer can report what it paid you on a 1099 at year end.
Why it matters
A W-9 request is the signal that no tax will be withheld from the payments that follow, so the tax is yours to plan for. Only give one to a party that is actually paying you; a W-9 request from a stranger is a common identity-theft setup.