On a hot, muggy day, the air becomes “thinner” or less dense, and its density at a pilot’s location is equivalent to a higher altitude in the standard atmosphere.  It is hazardous to aircraft during takeoff and climb because:

- Aircraft power is reduced. The engine will ingest less air to support combustion.

- Aircraft thrust is reduced.  A propeller will have less "grip" on the air, while a jet engine will will exhaust less mass.

- Lift is reduced.  The thinner air will exert less upward force on the airfoils.

As a result, a longer takeoff and landing roll is required, especially for a fully-loaded aircraft.  After takeoff, the aircraft will have a smaller rate of climb and will have a lower service ceiling.

Density altitude is usually reported at each AWOS/ASOS station in the Remarks section of the METAR, if the value is greater than 1000ft higher than the elevation of the airfield.  Here's an example:

METAR KMSY 291400Z AUTO 18006KT 10SM CLR 28/13 A3001 RMK SLP161 DENSITY ALT 1000FT