Oh! I see, now. The messages weren't
flagged at all; as Barry said, you somehow managed to get the message
priority set to "high". That dropdown menu of which he speaks has a single exclamation mark for routine priority (the default condition), a dash for low priority, and double exclamation marks for high priority.
Still, as far as what does it mean, Mail.app and all the smtp servers and intervening routers along the way don't care; it's not like messages get placed higher or lower in a queue or anything before being transmitted from router to router or anything like that; all it does is provide an indicator to the recipient reading the message that you thought the message you wrote was important.
Now, if you don't have a priority field being displayed in your new message composition window, when you are composing a new message, click on the small rectangle at the lower left of your message header region, click "Customize" and checkbox the fields ("Priority" being one of them) you might want, then click OK.
If you haven't had the message priority drop down menu displayed, sorry, I cannot proffer any scenarios of how you might have
inadvertently marked such a message as high priority; it would have to be a pretty deliberate action of going under "Message" in the menu bar, mousing over "Mark" and then selecting "High Priority" from the subsequent popup menu; there are no keyboard equivalents. I, personally, have neither experienced nor read about others having a problem like this, where Mail.app was randomly assigning priorities to sent messages without user intervention.