“Bend over Backwards” means to work very hard to accomplish something.
Example of use: “We bent over backwards to help him, and he never ever thanked us”.
Unless you are extremely flexible, actually bending over backwards is quite a feat. It’s not at all surprising that the origin of the idiom “bend over backwards” is in gymnastics. The term was used as early as 920 CE to compare the athletic act of back bending with an expenditure of effort to ensure that something went as planned.