The BINARY operator is a shorthand for a COLLATE clause. For example, BINARY 'x' is equivalent to 'x' COLLATE y, where y is the name of an appropriate binary collation. For example, assuming that column a is of character set latin1, these two queries have the same effect:
SELECT * FROM t1 ORDER BY BINARY a; SELECT * FROM t1 ORDER BY a COLLATE latin1_bin;
Note: Every character set has a binary collation.