Snapchat touts itself as being the "fastest way to share a moment with friends." While you can share moments with a variety of apps, Snapchat sets itself apart from the rest by allowing the sender to control how long that message will display on the recipients phone. Users sending images have the option for the image to display up to 10 seconds. Regardless of the specific time you set, the image is supposed to be deleted once that clock runs out.
With that in mind, a recent report is now showing that these images are not actually being deleted from your phone. The work is being done by Decipher Forensics who note that while the app mentions they deleted the image, it is actually being assigned a new file extension and kept within the app. According to Richard Hickman, the Snapchat app has a folder called RECEIVED_IMAGES_SNAPS and the images are being tucked away with a .NOMEDIA file extension.
The key here, while these are not going to be visible by the average user, they are there and can be found. The Snapchat app is available for Android as well as iOS, however as of now it looks like the work has been done on the Android side. Hickman has said he perfected the steps to extract these images on an Android device and is now setting his sights on the iOS version. Basically, with a little work (and some money) parents, lawyers and the police can get access to these supposed deleted images.
Interestingly enough, Hickman also talked about how images that were taken (and deleted) using the default Android camera app were harder to find as compared to Snapchat images. Bottom line here, this isn't to say that Snapchat is bad or that it shouldn't be used, however this should make you think twice about sending any questionable images.