Certified pre-owned, and what the premium buys
You're paying for an inspection and more warranty. Whether it's worth it depends on the car.

A certified pre-owned car costs more than the same car uncertified. The question is what the difference buys.
Two things, mostly. An inspection performed to the manufacturer's checklist, with anything failing it repaired before sale. And an extension of warranty coverage beyond the original term, backed by the manufacturer rather than a third party.
Those are worth real money on a car with expensive systems and a reputation for needing them. They are worth considerably less on a car that is cheap to fix and unlikely to need it. The premium is roughly the same either way, which is why certification is a better deal on some cars than others.
Two cautions. Dealer-certified is not the same as manufacturer-certified, even when the paperwork looks similar; only one is backed by the maker and honoured at any franchised store. And a certified car is still a used car — certification means it passed a checklist on a particular day, not that it has no history.
Ask which programme it is, ask for the completed inspection sheet rather than a summary, and ask what the warranty actually covers and for how long from what date. A certified car whose seller cannot produce the inspection sheet has not really been certified in the sense that matters.