Hello, jBrummer!
Welcome to Apple Support Communities! From what I'm reading in your post, it looks like you're seeing a message about something being "kept" by the person you are chatting with, instead of the normal date & time that's usually there in the right margin of the iMessage screen. I would be curious about that, too! I am happy to help.
From what I can see, that's the message you get when you send something other than "plain text" to the person with whom you're chatting, and that person saves whatever you sent. For example, a voice message, a heartbeat, or a little picture you've drawn using the new enhanced iMessage features we just introduced with iOS 10. I tested this on my own iPhone, and saw a tiny blue "keep" right under the message with effects that I sent. When I tapped that, my husband saw the "kept" under my artistically-challenged smiley face drawing!
For more info on the fun new iMessage features, check out this document: Use message effects with iMessage on your iPhone, iPad, and iPod touch
Hope that helps! Have a great weekend!