There are many reasons and SQL query may fail; the following details one possible scenario:

MySQL configuration files include an option for max_allowed_packet.  3Essentials standard is 16MB, and all servers should be set to this.  If you're executing a SQL statement that you know is smaller than this, and you're still getting this error, please submit a support ticket regarding the issue.

The most commonplace you experience this is when a customer is using a SQL file created from mysqldump (from another provider) to import their data onto our databases.  The user may receive "ERROR 1153 at line 42: Got a packet bigger than 'max_allowed_packet'". 

To address this, mysqldump has a "--set-variable" option, which you can use to set a "max_allowed_packet" size matching the target server, then mysqldump will generate smaller commands. If the customer is migrating from another host, they can request their previous host to run the mysqldump with this option set.  If their previous host will not do this, the customer can import the oversized SQL dump to a local instance of MySQL on their computer (where they can set a large "max_allowed_packet"), and then re-export it using mysqldump with the correct settings.