You can determine the original status of an iPhone by checking the first character of the model number:

To find this information, you can:
Open the Settings app on the iPhone
Go to General, and About

Look for the "Model" field and the first letter.

M - Brand new device purchased directly from Apple
F - Refurbished device that has gone through Apple's refurbishing process
N - Replacement device provided by Apple due to a service request
P - Personalized device with custom engraving

Those are the most common. And here are others that are less common.

D - Device used for development or testing purposes
G - Device sold through a carrier or retailer (not directly from Apple)
J - Device sold through a specific sales channel or promotion
Q - Device used for quality assurance testing
R - Device used for regulatory testing
T - Device used for training or educational purposes