The red circle with a red exclamation point means a message was not sent. If you scroll through the conversation, off to the left of at least one of the messages you will see this same icon, the red circle with an exclamation point inside.
Herein, what does an exclamation point on a dashboard mean?
That's the tire pressure monitoring system light. It indicates that there is a disparity in your tire pressure, which typically means that at least one of them is losing air.
Why is there an exclamation point on my pictures?
It means that it's a compressed (lower resolution) copy of the original image, which is stored in iCloud. Images may also appear blurry. (It's not the end of the world.) To get rid of the exclamation point, you need to switch the storage option (in Settings > Photos) to "Download and Keep Originals".
What does a triangle with an exclamation mark mean in my car?
This symbol can appear extremely threatening, but often indicates something minor. It's represented by an exclamation mark inside a triangle, and can be either yellow or red. The red version will often also feature text to warn you what is wrong, and could be something serious like low oil pressure.