This has come up several times, and it probably will again, but I'll stick in here as well to maybe make it easier to find in the future....
What do those icons mean next to my messages in the sent folder?
Green arrows signify a successful SEND from your phone, normally to a phone on another carrier. You can't tell if the other phone actually received it, or if the message was opened, simply that it was successfully sent out from your phone.
The green check mark means sent, and delivered, to another Verizon phone. You still can't tell if the recipient OPENED the message, but you do know if was delivered and received on their phone.
The red X means it didn't get sent, for whatever reason.
As far as I can tell, the high priority doesn't get sent or delivered any faster, or with any greater urgency, but the exclamation point is added to catch your attention when you get the message.