If you're levelheaded, you're rational and calm. When two people are arguing bitterly, they often need someone who's unbiased and levelheaded to help them come to a reasonable compromise.
A levelheaded decision is one that you make after calm and judicious consideration, and if a company is looking for a levelheaded person to work in a hectic office environment, they want someone who stays unruffled even under pressure. Levelheaded dates from 1869, from the "balanced" sense of level.