Increased air temperature decreases air density or air pressure. Picture in your mind air molecules in the atmosphere. When it is cold out these molecules are very close together and when it is hot out they are further apart. The effect of this pressure difference caused by temperature is called density altitude.

One very hot days when you listen to an airports AWOS/ASOS or ATIS the density altitude is given a form of an altitude in feet. AS an example if you hear density altitude 2000ft, this means that at airport elevation whatever the elevation is, the hot air will act on the airplane as if it is flying at 2000ft.

Now, what does this mean to a pilot? Well, as you may know the higher an airplane is in the sky the less dense the air is. Less dense air affects airplanes because there is less mass (molecules) for the airfoils (propeller, wing, horizontal stablizer) to work with (the propeller and wing take 'less of a bite' out of the air). Increased temperature will most effect climb performance and engine output. This is why it is very important a pilot know the density altitude when on approach or landing. In both phases of flight a pilot can expect a higher ground speed at the same airspeed which results in a longer takeoff roll and landing roll-out.

To be aware of this phenomenon, while important for all pilots in all areas, is most critical at airports of high elevation. Pilot's in the western states (Arizona, New Mexico, Colorado for example) may take off from an airport with a elevation of already 3,000 to 6,000ft. Couple that with a high denisty altitude and you may be pushing a small airplane's limits to operate.

Hope that gave you some insight!

Aircraft taking off in hot climates need a longer takeoff roll because hot air is less dense, so the plane needs more speed to lift off the ground. The engines need to work harder too in order to produce the same amount of thrust as it would in a normal temperature because of the thin air.