爸 = 父 (father) on top + 巴 (bā) for the sound. The 父 radical is itself an old picture of a hand holding a stick or axe — the figure of authority in the household. Add the sound and you get 'dad'.
Like 妈妈, 爸爸 (bàba) is doubled and built from an easy baby sound (b/p). Together 爸爸妈妈 are your parents. More formally, parents are 父母 (fùmǔ, father-mother). And 先生 — literally 'born first' — became the word for 'mister/husband', while the warm everyday word for dad stays 爸爸.
The father radical (父) over a sound part — DAD.
爸爸妈妈 = mom and dad. The formal word for parents is 父母 (father-mother). Chinese, like most languages, builds 'dad' from a baby's easy b/p sound.