Welcome to the Support Communities!
I'm including for you the iPhone User Guide in the link below.
Pages 70 - 73 explain how the Photo App works, and pages 74 - 76 will walk you through the Camera App features.
Here are a few highlights:
Camera Roll album—photos and videos you took on iPhone, or saved from an email, text
message, webpage, or screenshot
Photo Stream albums—photos in My Photo Stream and your shared photo streams (see Photo
Stream on page 71)
Photo Library and other albums synced from your computer (see Syncing with iTunes on
Syncing with iTunes copies information from your computer to iPhone, and vice versa. You can sync by connecting iPhone to your computer, or you can set up iTunes to sync wirelessly with Wi-Fi. You can set iTunes to sync music, photos, videos, podcasts, apps, and more.
It appears from your question that you may have synced some photos to your iPhone from your computer.
If you delete the photo from the iPhone, it will not delete it from your computer.
I hope this information helps ....
Have a great day!