An NSAID when circulating in the body takes on a role of inflammation reduction.  It does so by using its chemical role as a blocking enzymes involved with the chemical reaction that makes up inflammation.  The enzyme it blocks, cyclooxygenase, would typically allow a larger byproduct of inflammation (also a gastric protective substance), prostaglandin to be produced. However, once introduced, the NSAID blocks the chain in the reaction, dropping the overall expansion of inflammation and its irritating, expanding chemicals so that less pain is a result.