家 is a roof (宀) with a pig (豕) underneath. In ancient agrarian China, a household kept its pig inside — livestock under your roof meant a settled, prosperous HOME. The pig was the sign you'd put down roots.
Family is the center of Chinese life, and 家 is everywhere: 我家 (my home/family), 家人 (family members), 回家 (go home), 国家 (nation — literally 'country-family'). 大家 means 'everyone' ('the big family') — a warm way Chinese addresses a group. 家 is also a suffix for experts: 作家 (writer), 画家 (painter).
A pig (豕) under a roof (宀) — livestock at home means a settled FAMILY.
大家 ('big family') is how you greet a group: 大家好 = 'Hello everyone!' And 国家 ('country-family') is the word for nation — to the Chinese, the state is the family writ large.