Yahoo Application State Plugin is installed with Yahoo! Messenger to tell Yahoo! web pages whether you have Yahoo Messenger installed or not, which version you have installed and you are logged in or not. According to Yahoo! Messenger information disclosure , only yahoo.com and their other services have access to this plugin.
In 2008-09 people reported that Firefox crashes when using Yahoo Mail. Yahoo Application State Plugin was reported and banned from add-on directory at Firefox. Yahoo updated the plugin and the problem was solved.
To update Yahoo Application State Plugin to latest version, you have to update Yahoo! Messenger to latest version. Kindly note that even if you update this plugin to latest version, Firefox may show this plugin as outdated. Do not worry about it.