It's one of those weather things that you not only have to know about to pass your checkride, it's one of those weather things that could save your tailfeathers someday. So, what exactly is this mysterious "density altitude?"
Let's say you're on the ground ready for takeoff. YOU know what the field elevation is, however, your airplane doesn't! Your plane's performance (takeoff distance, rate of climb, engine power) is greatly affected by the density of the air, that is, the density altitude. As air heats up, it expands and becomes less dense(thinner), just like air at higher altitudes. SOOOOOOOOO, on a hot summer day, your airplane will perform like it is at a higher altitude.
For example, if you start out at sea level on a 90-degree day, your airplane will perform as if you were taking off from an airport 2000' above sea level!!!
Take a look at the performance charts for takeoff distance and rate of climb in your aircraft's POH. You'll notice that as the temperature increases, performance decreases. That means on warmer days you'll need a little (sometimes a lot) more runway to get up and go. Again, this is because your airplane thinks it is at a higher altitude.
So on those hot summer days, keep density altitude in mind when planning your flight. On a hot summer day at a higher field elevation, you may be able to barely make it off the ground.
Personally, I completed nearly all of my initial training and flying from airports near sea level. However, the first time I took my father flying was in Denver, Colorado. My flight began at a field elevation that was higher than I'd ever previously flown! (5,512') Combine that with an air temperature of 85-degrees and my airplane was performing as if I was taking off at 7,000'msl. The Cessna 172 I had rented acted more like a Cessna 150 at sea level, not as much power, didn't climb as quickly and it didn't glide nearly as well as I was used to. That's becasue the air is thin at higher altitudes, and the warmer temperatures made it even thinner (less dense).
It's interesting to note that on some hot summer days, even the big jets are sometimes not able to takeoff from places like Denver, which has 12,000 feet of runway!
Same thing can happen in the deserts of the West. As they heat up in the summertime, density altitude can push the envelope of safety.
So does this mean that when it's cold outside your airplane will perform better? YES! Cold air is more dense. It provides more lift, your rate of climb will increase, and takeoff distance will be reduced.