King Ahab was a king in the northern kingdom of Israel. He was known for his ungodly ways. He married Jezebel, a very evil woman, and together they promoted the worship of Baal, which was against the worship of the true God of Israel.
Jezebel influenced King Ahab greatly. She led him into idolatry. For example, she promoted the worship of Baal in Israel which Ahab then allowed. She also used her wiles to get her way. In the case of Naboth's vineyard, she was the one who came up with the evil plan to kill Naboth so Ahab could have the land. So, overall, she pushed Ahab to be more wicked and ungodly.
At the end of the story, Ahab is killed when his ship is destroyed by the whale he's been hunting. This shows the danger of unchecked obsession and defiance of nature.
Black-ish is not based on a true story. It's a creation of the show's writers and producers, who came up with the concepts and characters for entertainment purposes.