Go to the Selections menu and chose "deselect" in Photoshop 5 or higher and I believe "none" in lower versions,or use the short cut keys. "Control + D" on the Pc,not sure about the Mac,but I think it,s similar "Command + D".Something like that. By the way the moving border around selections is often refered to as "marching ants".Which I think is a great descriptive term.