Photos that you take with the iPad you can delete in the Photos app via the trashcan icon.
But photos that are synced from a computer are treated differently, they can'y be deleted directly in the Photos app, the trashcan icon will be disabled for them. Instead they are deleted by not including them in your next photo sync - so if, for example, you selected and synced folder A from your computer via your computer's iTunes, to delete those photos from the iPad you would have to reconnect the iPad to your computer, deselect folder A in iTunes, and resync.
That also means that you have to select any photos that you want from your computer and sync them in one go - you can't sync folder A, and then sync folder B, as that would remove album A from the iPad and replace it with folder B ; you would have to select A and B and sync both together.