scientifically, family is creatures like yourself. I.e. Humans. apparently we come under the family category hominidae, which also includes apes like gibbons, chimpanzees and gorillas. Some people say apes ought to be given human rights as well, since they are in the same family.
I'm not a scientists though, so I generally think that family just means people.
Jesus was asked to go with his mother and sisters and brothers once and he replied that anyone who did the will of God was the same as his mother, sisters and brothers.
when we become Christians since we accept Jesus sacrifice for us on the cross by his blood we become family members. Everytime we eat and drink the lords supper together...we affirm we are family because it represents his body and his blood.