The best way to learn about the gargoyles is to either watch some episodes or ready about them here
http://www.s8.org/gargoyles/index.php
I can at least give you an overview of the basics, if you wish to make your own character.
Gargoyles are ancient beings, and for a long time, they lived with humans to protect their homes (many gargoyles lived in castles and helped guarded it). They were far more common in the 900's. The gargoyles from the TV series were cast in a spell to sleep as statues until the castle 'rises above the cloud'. Their original castle was bought by a billionaire named Xanatos, and he had the castle built on top of his building, which made the castle seem like it was above the clouds. So, the gargoyles awoke, thus beginning the series.
Gargoyles are only awake at night. No matter where they are or what they're doing, as soon as the sun rises, they will turn to stone for their sleep. If they are broken during their stone sleep, they will keep that injury or, if they're shattered, will never return to being flesh and blood ever again. So, they have to find rest before they turn to stone for the day. During this time, if they were hurt, the injury usually heals itself well enough, though depending on the severity will have a scar or permanent disability because of it. Gargoyles are normally very noble, and they are loyal. They stay in clans, and they treat each other with respect. They normally don't have use for names, but after waking up in the 2000's, the gargoyles chose names for themselves. Normally, they would call each other 'brother' or 'sister', even if they weren't related at all.
Gargoyles can be a range of things. There are gargoyles that are nagas, pink, gold, griffons, etc. There's a range the characters can be.
When the sun sets, a thin layer of stone cracks, and the gargoyles break out of the stone to 'wake up'.
For more details about gargoyles, please refer to the website provided. There's lots of details for them, especially if you want anything close to the show.
Thanks for the interest!!!