If you’d like to share personal photos, but only briefly, then a service like SnapShot can help. Images are visible for only a set period of time before they disappear forever. (In theory, anyway.)
Yovo for iOS is based around the same idea. Take an image, add a caption or blur, set an expiry time and select your recipients. But it also includes "D-fence", a clever technology which prevents users taking clear screenshots.
This works by using a series of bars to obscure most of your image. The app moves these bars across the picture so quickly that your eyes just see the original image, with maybe a little flicker. But if anyone takes a screenshot, they’ll get mostly bars and very little image: not much use at all.
This doesn’t offer any guarantees, of course. A recipient could take several screenshots, or maybe just use another device to video the screen.
Right now Yovo can only share images between iOS devices, too, although apparently an Android build is coming soon.
If you need to securely share more than just pictures, you might be interested in CONTENTGUARD, an iOS and Android app from the same company.
This supports sharing images (PNG, JPG) and documents (PDF, DOC, DOCX, XLS, XLSX, PPT, PPTX) with your choice of recipients, again for a specified amount of time only -- anything from one minute to a month.
Your files are encrypted and sent directly to your recipients, who must verify their identities before they’re able to view them.
There’s no "D-fence" screen protection here, just an option to warn you "if the recipient tries to take an unauthorized screen capture". Still, CONTENTGUARD is an interesting free app which has plenty to offer both home and business users.