The Firebending symbol."The symbol for fire and Firebending is a stylized, tulip-shaped flame forked into three tongues that curve outward like flower petals, with a spiral at the base (to signify that fire is a source of life not just destruction as mentioned by the Sun Warriors)." Fire as stated by the Sun Warriors is ment to be a way of life that is why a tulip is shown inside the flames.
"In a way, this symbol vaguely resembles a seated Badgermole" This may be because the badgermoles as [mentioned by Toph] used earthbending not only to fight but as a way to communicate with the earth and to extend their senses therefore by using a seated badgemole it shows that earthbending is a way of being one with the earth. i believe that badgermoles is the original source of bending (Communication with the earth).
"It also shows how the moon and ocean spirit work together" The moon is symbolized by the spherical border while the ocean spirit is symbolized by the picture of an ocean and it also shows water bending philosphy about ying and yang or push and pull.
The Airbending symbol.Airbenders have the philosophy that theres always a way around something, that is why there is 3 air symbols showing that there always a way around a problem.
The parts not quoted are my opinions and some have been made into edits on the actual pages. i hope these representations or intrepretations of the symbols of all the bendings can be apreciated.
these images are not owned by me they are owned by Avatar the Last Airbender or Nick.com and i got these images form Aavtar wiki and the quoted parts by Avatar Wiki