Verifying the disk is the same as running scandisk on Windows 9x or chkdsk on Windows NT, if that makes in any clearer. Essentially it verifies that the file system is intact, with no inconsistencies. It doesn't check the contents of files on the disk, just the structure of the file system and the drives logical state.
When you are verifying the disk, Finder and any other applications running off of the disk being verified may become unresponsive because the disk is being checked for consistency. There is nothing wrong with that in of itself. Does Finder eventually recover on its own, and does Disk Utility give a report as to the condition of the disk after completion of the disk check?