Add-on sync allows you to easily keep the same set of Firefox add-ons on all of your devices. When enabled, add-on sync will install, uninstall, enable or disable add-ons on all Sync-connected devices as you make changes to them. For example, if you install Adblock Plus on one computer, Adblock Plus will get installed on your other computers.
Add-on sync only works between similar Firefox installations. For example, if you install an add-on on desktop Firefox, it will only sync to other desktops, not to your Android device running Firefox.
If you haven't set up a Sync account yet, add-on sync will be turned on when you create your account (see How do I set up Sync on my computer?). If you already have a Sync account, you can enable (or check the status of) add-on sync by following these simple steps on all the devices that have add-ons that you want to sync.
These instructions are for desktop Firefox.
If you install add-ons directly from https://addons.mozilla.org, your add-ons should always sync. Add-ons installed from other sites or installed by other programs (your security software, for example) will not be synchronized.
For more technical information, see Add-on Sync on Mozilla's wiki.