The tagged red exclamation mark on someones pictures means that the pics, vids, etc are NSFW (Not Suitable For Work). Most of the time they are pics tagged for nudity or profanity. Snapchat's security in their full disclosure relates the red exclamation mark with 'mature content' and gives a content warning to the receiving user saying "the red exclamation mark on this Story indicates that Stories posted by this user may not be suitable for sensitive viewers. Do you wish to continue? After selecting 'Yes', you will never be prompted again."
Beware when opening these messages and it might not be a good idea to view these at work, around children or other 'sensitive viewers'. Messages with this exclamation mark usually come from people known to send explicit messages.
Some forums online say the exclamation mark means that your message has not been sent. Test it with your friends by turning off your phone's wifi and trying to send a snap. If you see an exclamation point, it will prove or disprove this version.