As with many computer problems, a lack of sound on a Facebook video can be caused by many different factors. By identifying where exactly the problem lies you can more easily come up with a fix -- playing other videos on Facebook, videos on different websites and videos stored locally on your computer should indicate the root cause of the issue.
Video Problem
If the lack of sound only occurs on one video on Facebook (other videos on the site play without problems), check the volume setting for the clip (hover the mouse cursor over the video to see the volume control). If the volume is set correctly, then it's likely that the file has been encoded or uploaded without any audio attached. If the video is one of your own uploads, check the source file and try processing and uploading it again. If the video belongs to someone else, check with the user in question to see if the clip should have sound and to flag the problem.
Video of the Day
Facebook Problem
If the lack of sound only occurs on Facebook videos (videos from other sites and programs play without problems), check the volume level on the clips you're trying to watch (hover the mouse cursor over the video to bring up the volume controls). Check the Facebook help pages to see if there are any known issues the site is currently experiencing. Disable any Facebook-related extensions you have installed on your browser (check your browser's documentation for details on how to do this) and then log out and back in to Facebook to refresh some of the site's settings. Clearing your browser's cache and cookies may also help to resolve the problem.
Browser Problem
If you're not getting sound in any video in your browser, but hearing sound from video played from local desktop apps, your browser software is likely to be at fault (you can easily test for this by trying an alternative browser to see if the issue is cleared up). Check the browser's volume level in the Windows Volume Mixer by clicking on the speaker icon in the notification area of the desktop. Uninstalling and reinstalling the browser, deleting its store of temporary cached data and cookies, and disabling browser extensions (particularly those relating to audio or video) may also help restore the sound. Ensure you are always running the latest version of your browser and any plugins running on top of it.
System Problem
No volume from any video on your system points to a problem with the operating system as a whole, particularly the codecs installed on top of it. Even if the problem is restricted to Facebook, a corrupted Windows file could be to blame. Launch the Windows Update component of Control Panel to ensure the latest updates have been downloaded and installed, and install the most recent drivers for your sound card and motherboard (from the manufacturer's official website). Check the volume settings within Windows (via the speaker icon in the notification area) as well as on any external speakers you have installed.