Other forms: bending over backwards; bends over backwards
To bend over backwards is to work extra hard to make something happen, particularly to help someone or to make them happy. If your smart friend bends over backwards to help you pass your math test, you owe her a huge thanks.
You might bend over backwards to avoid offending your delicate grandparents, or bend over backwards to help your dad clean the house before they come over for dinner. In both cases, you go all out — you throw yourself into the project with extra effort. This phrase dates from the turn of the twentieth century, and while its origin is vague, it's not hard to figure out how it came to mean "work hard to do something difficult."