The Phoenix, alongside it's extraordinary beauty, is very talented. One of it's well-known talents is the ability to control the heat it's body lets off. It can "singe your sword to your face" from great distances or can let you pet it just like you stroke your pet cat -- without any heat blister at all!

As Professor Albus Dumbledore (or Fawkes, his pet Phoenix) has proven to the Ministry of Magic in the past, it can bring it's wings together to propel huge streams of fire.

Another ability that is less-known is the bird's shrilling call. It can shriek so loud that anyone around is "brought to tears" or can't hear clearly for days or in worse cases, weeks.

The last ability is it's most famous. The Phoenix bird has the great ability to, when it dies, it bursts into flames and is reborn from its ashes. This, though, is something that we have already covered numerous times.

That is all of the known abilities of this wondrous bird. You can find some additional information in "Fantastic Beasts and Where to Find Them" by Newt Scammander.