This is a very complex poem comprised almost entirely of metaphors and symbols, which make it difficult to pin down any fixed meaning. One interpretation of the poem, however, is that it is all about the power of different kinds of knowledge, and that each different type of paper referred to represents or symbolizes a different type of knowledge.
For example, the paper in the first stanza symbolizes the written word which, metaphorically, "lets the light / shine through." This metaphor implies that knowledge in the form of the written word can help things to become clearer. The line, "Paper thinned by age or touching," also represents how fragile and precious this type of knowledge is.
Later in the poem, Dharker writes about "maps" with "borderlines (and) the marks / that rivers make." Maps in the poem could symbolize the type of knowledge that we use to orientate ourselves in the world. This could literally be geographical knowledge, but it could also be knowledge about who we are and where we want to go in life.
In terms of the structure of the poem, every stanza has four lines except for the last stanza, which is just one line. This suggests that Dharker wanted the last line, "turned into your skin," to stand out. One of the possible ideas in this poem, an extension of the theme of knowledge, is that the best type of knowledge is that which exists between ourselves, on an interpersonal level. In other words, the best type of knowledge is the emotional knowledge that exists within and is developed through human relationships. This is the type of knowledge which leads to empathy and sympathy. Towards the end of the poem, the paper that Dharker has been using to symbolize different kinds of knowledge changes to human skin. The isolation of the final line, in a stanza of its own, is perhaps to emphasize how this interpersonal, emotional knowledge is the most important and vital kind of knowledge we have.