The previous owner should have wiped the iPhone clean, so you could set it up from scratch,
If they did not do this its possible the iPhone may lock with activation lock and be unusable.
The first thing to check when acquiring a new iPhone is whether or not the previous owner's ID is still signed in to anything. It should not be.
Before doing anything else, check if there is an Apple ID different to your won signed in for iCloud in Settings->Account(top of settings) and verify what Apple ID is signed in for iCloud there
If there is the previous owner's Apple ID there, you will not be able to remove it without its password, and the iPhone can potentially be locked by the previous owner at any moment, rendering it unusable.
You will need to contact the previous owner and have them follow the steps here: What to do before you sell or give away your iPhone, iPad, or iPod touch - Apple Support
If the previous owner's Apple ID does not appear there, you can wipe it yourself, and start over, to remove any possible presence of the previous owner's Apple ID from the device. There can be no apps that he purchases left on the device either as those will be tied to their Apple ID and cannot be used by you.