What is ment by backing up information?

To "back up" something has two meanings

In the context of information

1) To provide evidence which proves that the information is true.

e.g "It's interesting what you're saying, but can you back any of it up?"

2) To create a copy of the information, in case the original is lost or destroyed.

e.g "You need to make sure you back up all of your research data."

In the context of people it means to provide assistance to someone who is in a conflict, in order to help them win that conflict.

e.g "No one believed my friend at first, but once I backed her up, people realised she was telling the truth"

"Hey, why didn't you back me up?"

Note the Word order.

Back me/you/him/her/it/them/NAME up (Not Back up SOMEONE)

Back up SOMETHING/ Back SOMETHING up (both are fine)