If you would need to escape special characters like '_' (underscore), as it was in my case, and you are not willing/not able to define an ESCAPE clause, you may wish to enclose the special character with square brackets '[' and ']'.
This explains the meaning of the "weird" string '[[]' - it just embraces the '[' character with square brackets, effectively escaping it.
My use case was to specify the name of a stored procedure with underscores in it as a filter criteria for the Profiler. So I've put string '%name[_]of[_]a[_]stored[_]procedure%' in a TextData LIKE field and it gave me trace results I wanted to achieve.
Here is a good example from the documentation: LIKE (Transact-SQL) - Using Wildcard Characters As Literals