To back somebody / something up
which means to support somebody or something; to say that what somebody says is true.
I'll back you up if they don't believe you.
The writer doesn't back up his opinions with examples.
This verb can also be used with the meaning of preparing a copy of a file or program which can be used if the main one fails. I'm sure you've all heard of a backup copy (using the word as an adjective).
Example: It's a good idea to back up your files on a memory stick.