I plugged an iphone 5s into my laptop and it says, erase and sync with library. What does this mean?

Will it erase everything and make the iPhone into factory settings? Or only music, videos and apps?

i don't want to lose information such as the apple id, passwords and so forth.

It means it will erase all your current things and sync what's on your computer. For instance if you have music on your phone and go to sync it, it will erase all the music currently on your phone and sync what's in your iTunes library. (but you can customize which albums or artists to sync) This isn't a problem unless what you want to keep on your phone isn't on the computer your syncing it to. But if you don't want to erase certain things you can check off which things to sync, like maybe you want to sync your music library but not your movies or contacts, then don't check those off. I guess this explanation seems more complicated than it actually is. Before you attempt this I'd suggest backing up your phone to your computer (on the iTunes application) so if something does go wrong you can back it up and have everything you had on it initially.