Ouroboros, the snake eating its own tail, is a fertile symbol (metaphor, analogy, projection object) that can be understood in many ways.
One is as an analogy for the process of self-inquiry.
In the beginning, it appears that there is a separate self here inquiring, investigating, exploring and so on. But the process itself includes the annihilation of this sense of a separate self. Eventually, even that is seen as just something on the inside of a story, something that appears real only because it is taken as real, a thought placed on top of pure perception, filtering it into what appears as an I here and Other there.
The process of inquiry, and any spiritual practice leading to Ground noticing itself, is a process eating itself up. The separate self, the doer, that appears to initiate and engage in it, is revealed as never having been there in the first place.