There are quite a few good reasons to use a pole dance crash mat. Check out the video below...this is somewhat funny but can be a dangerous thing resulting in bad, even tragic injury):
Crash mats are designed to absorb some of the shock from a fall, not all. Care should be taken and strength built , proper technique learned and all pole dance safety precautions heeded. You should review all of the safety musts for pole dancing and always use a spotter and a thick, quality mat when learning inversions and new aerial tricks.
Mats come in several different thicknesses, some portable, others not so portable; they also come in round and square shapes to fit around your pole.
Here is an example of a quality, 5" thick, 5' round pink Pole Dance Crash Mat: This particular mat is manufactured by PoleCrashMats and is deisgned to be portable, is made with a high quality foam, has a dura-cover option that can't be punctured by heels and is firm enough to walk on. These sell for about $230 on Amazon.
Mats cost anywhere from $150 to $300 depending on the thickness, area covered and manufacturer. You can find them on Amazon, Ebay or through websites such as The Pole Dancing Shop (click on the image below) or Sensual Fitness Classes who have a wide selection to choose from.
There is also another mat that comes in 9' diameter and 14" thick created for serious aerial artists! This is manufactured by Poleexercise (UK).
All of their Lulu mats come with a surface firm enough to walk on and also designed for use with heels. The foam is also designed dually with a softer underside if you are practicing drops (for a gentler landing!)