The Regular Expressions mode lets you perform batch renaming using regular expressions to specify search and replace patterns.
The example above shows a very simple regular expression that has been used to remove the underscore from the original filenames. The Old name pattern of (.*)_(.*) uses parentheses to tag two "match anything" expressions, and the \1\2 in the New name pattern inserts the values of the two tagged expressions in the new name.
An extension Directory Opus provides is the ability to perform a repeating search and replace using regular expressions. The above example will only remove a single underscore, but if you wanted to remove all underscores from the source name, you can append a # (pound/hash) sign to the Old name pattern. This causes Opus to repeat the search and replace until the new filename no longer changes.
See the Regular Expression Syntax reference page for more information about using regular expressions. Additional information can be found in Microsoft's introduction to TR1 ECMAScript (the flavor of regular expressions that Opus uses by default) for more information, and you can ask on the Opus Resource Centre if you need help.