Pencils are made of graphite, a soft mineral form of carbon which rubs off to form lines on the page. The paper itself is just flattened cellulose fibers, the supporting material of woody plants, and usually some amount of clay filler.
An eraser is an abrasive, sticky rubber substance that pulls the graphite marks off the paper. In doing so it will somewhat damage the paper fibers which, if done enough in one spot, can actually tear a hole into the page. Before that point though it usually at least damages the fibers making that area of the sheet rougher. The more rough paper more readily rubs off graphite making marks on that area darker.
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