To delete a photo album that you created on the iPhone, open the Photos app and select Albums in the bottom right corner of the window. This should allow you to view all the photo albums on the iPhone. Next, tap Edit in the top right corner of the window. Any albums that you created should now have a red circle to the left of the album. Tap the red circle then tap on the Delete option that appears. This will remove the album from the iPhone.
If a photo album appeared on your iPhone after syncing with iTunes on your computer, you may not be able to delete the album as described above. Since iTunes created the album, you will likely need to use iTunes to delete the album. Connect your iPhone to your computer and launch iTunes. Select your iPhone from the Devices list and select the Photos tab near the top right of the window. You will see an option to “Sync Photos from”, which allows you to select a folder on your computer to use for syncing photos. If the folder shown in the drop-down list matches the name of the album you want removed from your iPhone, uncheck the box for Sync Photos and select Apply or Sync in the bottom right of the window. This will remove the album and all the pictures in that album from your iPhone.
If iTunes is not currently syncing photos from a folder, you can remove an unwanted album with a slightly different process. On your computer, create a folder with the same name as the album you want to delete from your iPhone. On the Photos tab in iTunes, select the empty folder you just created and click Apply. This should delete the album and its photos from the iPhone.