I'm going to assume you're wanting to do this on an iPhone. With that assumption, do the following:
1. Initiate the Photos app on your device.
2. Select "Albums" at the bottom right corner.
3. Select the album containing the photo you want to remove.
4. Tap on "Select" in the upper right corner.
5. Select the photo you want to remove.
6. Select "Add To" at the bottom of the screen.
7. Select the place where you want the photo to appear.
By the way, I did this while running iOS 10 so the wording and overall procedure may be slightly different.