What is the purpose of putting an ‘N’ in front of function parameters in TSQL?

It indicates a “nationalized” a.k.a. unicode string constant.

http://support.microsoft.com/kb/239530

When dealing with Unicode string constants in SQL Server you must precede all Unicode strings with a capital letter N, as documented in the SQL Server Books Online topic “Using Unicode Data”.

http://msdn.microsoft.com/en-us/library/aa276823%28SQL.80%29.aspx

nchar and nvarchar

Character data types that are either fixed-length (nchar) or variable-length (nvarchar) Unicode data and use the UNICODE UCS-2 character set.

nchar(n)

Fixed-length Unicode character data of n characters. n must be a value from 1 through 4,000. Storage size is two times n bytes. The SQL-92 synonyms for nchar are national char and national character.

nvarchar(n)

Variable-length Unicode character data of n characters. n must be a value from 1 through 4,000. Storage size, in bytes, is two times the number of characters entered. The data entered can be 0 characters in length. The SQL-92 synonyms for nvarchar are national char varying and national character varying.