Some major uses of this phrasal verb are linked to the idea of supporting or helping somebody or something. For example, you can help a person in a difficult situation, or affirm that something they have said is true by 'backing them up.' You can also support something you yourself have said by 'backing it up' with research or evidence. This theme can also cover supporting or safeguarding important work or files stored on a computer. If you 'back up' something in this context, you make a digital copy in case anything happens to the original.
This phrasal verb also has other common uses. For example, if something is entering from one end but is stuck at the other, you can say that it is 'backed up.' That can refer variously to traffic, a toilet, a nose, etc.
'Back up' can also be used to refer to moving a vehicle backwards or asking somebody to repeat something in a conversation.
As the video shows, it is commonly used in both a social and professional context.