Is there a lock symbol at the top of the screen next to the battery indicator ? If there is, then depending on what you've got Settings > General > Use Side Switch To set to (rotation lock or mute notifications), then you can lock/unlock the rotation by the switch on the right hand side of the iPad above the volume switch, or via the taskbar : double-click the home button; slide from the left; and it's the icon far left; press home again to exit the taskbar. The function that isn't on the side switch is set via the taskbar instead : http://support.apple.com/kb/HT4085
If there isn't a lock symbol then try a reset : press and hold both the sleep and home buttons for about 10 to 15 seconds (ignore the red slider), after which the Apple logo should appear - you won't lose any content, it's the iPad equivalent of a reboot.
Sounds like you may have orientation locked on your iPad, so when you turn it the display remains as is.
If you are using an iPad with iOS 5 or later the easiest way to check is to double click the home button and swipe the dock icons left to right. You should see an icon in the bottom left - an arrow in a box - does it show a padlock? If so your orientation is locked, simply click the icon to unlock.