Plain English Meaning
The air is thinner than it should be for the airport's elevation. The airplane reacts as though it were taking off from a much higher field, even though the runway is where it has always been.
Full Definition
A condition in which the density altitude is significantly higher than the airport's actual elevation, meaning the air is less dense than standard. It occurs when some combination of high field elevation, high temperature, high humidity, or low atmospheric pressure causes the air to behave — from the airplane's perspective — as if the airport were located at a much higher altitude than it really is.