This is a commonly used English expression, particularly in informal contexts. Whilst it can be used in a literal sense it is most commonly used metaphorically.
The expression is used to express the act of doing everything possible. It denotes a willingness to do anything in order to make something a success, including in some cases to go to the extreme and actually do too much. It can be interpreted in both a positive and a negative way. Sometimes it is used to express that someone is committed to something and is hard-working but in others it can be used to suggest that someone is only doing something in order to receive a reward for having done so.
This colloquial expression is fairly modern and was first used in the United States in the 1920s. The origin of the expression is still widely debated. The most common suggestion is that it links to the fields of gymnastics and acrobatics where contortionists who, in order to impress the audience and remain in work, would contort into strange positions. Thus the idea is that they would try their utmost to bend in any possible way in order to be successful.
An example of the usage of this expression can be found in a quote from American singer Dolly Parton who stated “I don’t make people bend over backwards, and I don’t like that in people. I am definitely no diva.”