I want to start a gambling website. Is it legal? What is considered Gambling?

What you describe is generally referred under many states' laws as a "game of chance," which is usually forbidden to those without a license. Moreover, gambling of any kind (internet or otherwise) is highly regulated on a state by state basis. That is why you will notice that most internet gambling operations allegedly operate out of off shore entities (e.g., Antigua). That is because to do so in the US might expose the principals to liability under each state's laws in which the site is accessible. Online gambling is also problematic considering the US courts' and government's use of the federal Federal Wire Act to punish online gambling operations, though such approach is being contested in the WTO.

Disclaimer: This answer is for informational purposes only and does not constitute general or specific legal advice, nor create an attorney client relationship.