There are at least two people in the Bible named Nadab. One was a son of Aaron and the other was a king.
Nadab, the son of Aaron, was consecrated a priest along with his three brothers, Abihu, Eleazar, and Ithamar, to minister at the Tabernacle (Ex. 28:1).
Later, though, Nadab, who was Aaron's first son, and Abihu were guilty of offering "profane fire before the Lord, such as He had not authorized", in the Sinai desert. Both Nadab and Abihu died when "Fire came forth from the Lord's presence and consumed them." (Lev. 10:1-2).
The other Nadab was the son of King Jeroboam and became the second king of the northern kingdom of Israel.
King Nadab reigned for two years. Like his father, he worshiped false idols and led the people of Israel into sin. He was assassinated by Baasha while he was with Israel's army during its attack on the Philistine city of Gibbethon. Baasha then became the next king.
The story of King Nadab is found in 1 Kings, chapter 15.