What do you mean by "a program appeared" ? Is this a window on the desktop? A login prompt when you turn on the computer? An actual application you open for some reason?
What exactly are you seeing? Can you take a screen shot?
If the previous owner did not completely wipe it, it may still be logged in the college account somewhere, but hard to say whether that would prevent you from doing anything else. Since we don't know exactly what it's saying or when it's appearing.
If you are correctly logged in with your Apple Account at System Settings ➜ Account, and your user is an administrator you may be able to erase the Mac and set it up again.
click here ➜ What to do before you sell, give away, trade in, or recycle your Mac - Apple Support
It's clear by your description you are not very knowledgeable with computers so it would help if you could clearly explain what exactly you are seeing