A combination of the words "family" and "damn," placed in such a way so that friends and acquaintances who have heard you refer to yours can mistakenly mix the syllables and call them your "damn family".
"So my fandamily is coming in for the holidays. Aunt Ruth probably hasn't shaved her beard in a while."
"Man, you have a weird damn family...err.."
Your family, usually referring to the whole family, more specifically a large family.
Especially used in instances when your large family becomes a hassle or annoyance.
"On Thanksgiving it takes a week to make enough food for the whole fandamily!"
"We went on vacation and the whole fandamily had to squeeze in the car for the whole ride."
"I went to the Family Reunion and had to deal wit my whole fandamily."
"We showed up at the wedding wit the whole fandamily."