If you are running FF 40.0.3 or higher, this extension may not be available to you due to the new FF signing restriction policies: http://www.ghacks.net/2015/02/10/mozilla-to-require-add-ons-to-be-signed-in-the-future/

[b]When will this take effect? [/b] Mozilla plans to display warning messages in the second quarter of 2015, likely with the release of Firefox 39 which, according to the Firefox release schedule, will land June 30, 2015.

As avast online security is a feature of avast, you normally will see it come up for the first time when avast is just installed, after which your browser will ask to run AOS. You either allow it to run or deny at that time. Go to Tools>Addons>Extensions in FF and see if it is listed in there under the Add-ons Manager Tab. If it is, then click Enable and restart FF to allow it to run in your browser as it will be disabled if Deny is used at the time of install. If Deny is used, then you will not see the extension running in FF as it has already been disabled.

[EDIT:] Fixed composition