Normally, you can tap and hold any photo in the Gallery app for Android to access the option to delete. That option may not appear for all of your photos. That’s because the Gallery may not only show images on your SD card, but images stored on a web service as well.
In cases like this, you’ll need to delete the photos from whatever service they were uploaded to via the web interface. The most common service that does this for Android users is the Google Plus app. Google Plus has functionality that syncs photos with Google Plus via Instant Upload. If the menu to delete a photo doesn’t appear and there is a Picasa logo on the thumbnail to the image, you will need to delete the image from the Google Plus service. To do so, simply visit your Google Plus profile and remove the images from your personal Instant Upload page.
If you want to keep your images in your Google Plus profile, but you don’t want them displayed within the Gallery app, you can simply disable photo syncing by going to Settings > Accounts. From there, you can select the Google account you are using, then uncheck the Sync Picasa Web Albums option.