Can be used in two different ways. One way being shock or surprise. The other way is more of a stubborn, selfpride thing meaning you refuse to do something, say something, believe something, etc.
Well, I'll be damned. Kenny fell in love with a hoe.
The veteran Confederates watch as the new VMI cadets hold their formation in the midst of murderous Yankee canon fire
Veteran 1: I'll be damned.
Veteran 2: If I didn't see it with my own eyes...
This phrase was first started by southern Africans at the time of 17th century. People usually use it now when they see something that they thought was impossible, has been done. Or sometimes it can be used in a manner of not agreeing to something, in case of apologizing etc.