The characters literally combine to mean “not (不) leave behind (遗) any surplus (余) strength (力)”. This creates a vivid picture of someone using every last bit of their power, influence, and resources to accomplish a goal, holding nothing in reserve.
不遗余力 is more than just “trying hard”; it reflects a deeply ingrained cultural value of diligence, perseverance, and total commitment, especially when working towards a collective goal or fulfilling a serious duty. It is a high form of praise that acknowledges a person's complete and selfless dedication. To compare, the English phrase “to go the extra mile” implies doing more than what is required. 不遗余力, however, focuses on the intensity and totality of the effort itself. It's about using 100% of your capacity for the required task, not necessarily exceeding its scope. It highlights a spirit of exhaustive effort and is often associated with the Confucian values of dedication (忠, zhōng) and perseverance. Praising someone with this term is a sign of deep respect for their work ethic.
This is a formal idiom (chengyu) and carries significant weight.