to give your support to a project, plan, or decision etc
A planned ban on street drinking in a town centre has been backed by the police and crime commissioner.
to sign a document to show acceptance or show financial responsibility for someone or something
We can only accept this as security if you back it first.
to sign the back of a negotiable instrument (=document which represents an intangible right of payment); to endorse
The instrument in question was backed with the instruction "pay to the order of Emily Burns".