The most common complaint we get from clients is that Facebook is rejecting their video upload based on audio copyright problems. If you have created a video and added music to the background, you need to ensure that the music is in the public domain. if it isn't then you are in violation of copyright laws and Facebook will reject your video. The easiest solution is to remove the background music. If you really want add music to your video, there are many audio services available for hire.
If you are also worried about video uploads to YouTube, YouTube also has some specific information about audio copyrights and how to use music that is copyrighted legally: https://www.youtube.com/watch?v=kqq_oq6QWZI