Upgrading site from 2.3.2636 to 2.4.2684
Probably a timeout on the MySQL side. You could try making a database backup manually and then changing this config value to false before trying the update again: http://buildwithcraft.com/docs/config-settings#backupDbOnUpdate

That way Craft will skip the database backup during the update, saving some time and hopefully preventing a timeout. Just remember to make a backup every time you update from then on though.