SET PASSWORD [FOR user] = PASSWORD('some password')

The SET PASSWORD statement assigns a password to an existing MySQL user account.

With no FOR clause, this statement sets the password for the current user. Any client that has connected to the server using a non-anonymous account can change the password for that account.

With a FOR clause, this statement sets the password for a specific account on the current server host. Only clients that have the UPDATE privilege for the mysql database can do this. The user value should be given in user_name@host_name format, where user_name and host_name are exactly as they are listed in the User and Host columns of the mysql.user table entry. For example, if you had an entry with User and Host column values of 'bob' and '%.loc.gov', you would write the statement like this:

SET PASSWORD FOR 'bob'@'%.loc.gov' = PASSWORD('newpass');

That is equivalent to the following statements:

UPDATE mysql.user SET Password=PASSWORD('newpass')
  WHERE User='bob' AND Host='%.loc.gov';
FLUSH PRIVILEGES;

Note: If you are connecting to a MySQL 4.1 or later server using a pre-4.1 client program, do not use the preceding SET PASSWORD or UPDATE statement without reading Section 5.7.9, “Password Hashing as of MySQL 4.1”, first. The password format changed in MySQL 4.1, and under certain circumstances it is possible that if you change your password, you might not be able to connect to the server afterward.

You can see which account the server authenticated you as by executing SELECT CURRENT_USER().