To delete a photo or video from your album, open the Album tab and tap the photo or video you'd like to delete. Tap the menu icon in the top-right corner, then tap "Delete". The app only allows grandparents and other relatives to delete photos/videos they uploaded.
Currently, photos and videos can only be deleted through the app version of FamilyAlbum. This includes photos/videos uploaded from a computer using FamilyAlbum Premium.