As Ron said, when water hits paper, it will carry the soluble discoloration in the paper with it, to the wet/dry boundary. That boundary is called the tide line, and usually has a higher concentration of "junk" in it,f and so is darker.
Sometimes when the paper is cleaned the paper has a greyish/translucent tone where the tideline was. I don't really know why - could be that the higher concentration of acids at the tideline causes that part of the paper to be a bit more degraded than the rest.
If the water is dirty, and carries particles of grime/soot or whatever, it may be impossible to remove the stain as the particles become irreversibly embedded in the paper web.
Elmer Eusman, of the Library of Congress, has shown that tidelines can be produced in pure
cellulose paper (Whatman's filter paper) using
distilled water. His inference was that since paper begins to oxidize as soon as it is made, oxidized parts of the paper (hornification
products)are moved to the edge of the wetted area
of the paper,where they concentrate. He demonstrated that the tidelines that they caused
could be seen, first in UV light and later, as they aged, they darkened and became visible in
ordinary light. Any soluable dirt in the paper or
dirt in the water could, as Rebecca noted, also
contribute to the creation of such lines. Since
any paper can form tidelines, if it is wetted, locally, great care must be taken to keep liquid water away from paper. Solvents applied to some papers can move additives, such as optical brighteners, also causing tidelines, over time.