Recalling and remembering the past is the job of one thing; memory. embarrassing memories and terrible dates are only two examples of experiences that might be recalled thanks to your brain's memory.
Both the information and events you recall as well as your brain's capacity to hold them all are included by the term "memory." You can remember someone's name if you have an excellent recall for their names. It's also a sign that you had a wonderful time working at that one McDonald's over your summer break. The capacity of a computer's memory has also come to be referred to as its "memory." There is no evidence that computers are fond of their previous software.
The author is saying that the last bits of life that remain will be snuffed out by what is left of his youth. For this reason the narrator includes the line about being consumed by that which it was nourished by. This line is referring to the narrator's life being nourished by the youth that is now represented by ashes that put out the fire of life.