Simba was a cub when his father died. He was from the royal bloodline, which is why he was the next choice for king. Unfortunately Scar was a douche and took the throne first. Then some stuff happened, Simba ate some bugs, Scar got eaten by hungry hyenas, blah blah and then Simba was able to be king!
It's mixing classic medieval politics with the African lion prides.
In a pride only the strongest are able to be the pride leader and they fight for it in the actual wild until the current leader either surrenders or is killed.
When a king dies either his first born son is king or the next person in line below him tries to usurp the throne.
Now what happens in the Lion king is mix of two, Simba comes from a royal blood line his father being the king of I guess the most powerful pride or kingdom in Africa so Simba would have been next in line to lead after his father died or stepped down, which makes him a crown prince of sorts, but his uncle scar usurped the throne from him by killing his father and banishing Simba.
Then Simba became stronger and returned from exile and challenged scar and killed him, taking leadership from him and proving he was the strongest, but also retaking his throne so to speak.