First you should know what you're doing. This is not something you want to just jump in and start messing with. See the forums for more information.
If you are on a remote computer ssh into your server and run these commands (starting as root).
su - zimbra zmlocalconfig -s | grep mysql | grep password
The output will look something like this.
mysql_logger_root_password = AWHZ60JYaBw8_hVkA9NDVGh0irmp7xVz mysql_root_password = lkAd7vkYI.Q_VeWt8uyL9kj0 zimbra_logger_mysql_password = 2iiyAVj3GeH0akkCe6M1o_HvY zimbra_mysql_password = uMv4EsNqPZdK5htERx97VY5m
Resetting_LDAP_&_MySQL_Passwords explains how to change the passwords if necessary.