A head start is a preferred position or an advantage, sometimes obtained by starting to do something before anyone else does. A runner with a head start may win a race even if she's not the fastest.
You'll get a head start on the 50-yard dash if you begin to run before your opponents do. You'll get a head start in life if your parents have the money and experience to send you to great schools and buy you lots of books. This second, figurative use of head start inspired the US preschool program called Head Start, which is intended to help poor kids get ahead early in their lives.