It means that He injured his hand so bad on his fingers that he could lose his hand because of this injury

Helped a lot! Thank you so much for your explanation:)

The sentence actually has errors. I understand that he had an injury to his hand. In that injury, there was a lot of tissue (skin and perhaps tendons) that came off (left behind). The writer of the sentence also indicates that he might lose his hand because of the injury. However, also might not lose the hand (indicated by the use of the word "potentially) A better way to write the sentence would be. He left behind a good deal of tissue off of his fingers, potentially a hand-losing injury. Personally, I would write about the incident differently. People can get get confused about the meaning when the sentence has a lot of information within it. This is called a "run on sentence". Here is how I would write and also speak it He lost a good deal of tissue off of his fingers. This is potentially a hand-losing injury. Also in your original sentence there is nothing in the wording that indicates he did or did not lose his hand. I hope this is helpful

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