If you have a vested interest in something, you have a personal stake in its success. You have a vested interest in your science project — if your invention works, you could be rich and famous.
Vested can also refer to something assigned to you. When a minister says "by the power vested in me by the State of Ohio, I now pronounce you husband and wife," he's referring to the legal authority he’s been given to marry people. Vested can also be a financial term. If you’re vested in your company's pension plan after working there 5 years, then even if you quit at 5 years, that pension money is yours to take with you.
