What does this equation mean?

When a reaction can plausibly form more than one product — partial versus complete oxidation, a straight-chain versus branched hydrocarbon, hydrogen versus oxygen evolution as a side reaction — “selectivity” names which pathway wins, and IUPAC defines it with no vocabulary that presumes anything about the catalyst’s intent: fractional selectivity for a given product is the extent-of-reaction rate toward that product divided by the sum of rates toward all products, $S_F$ = $\xi_i$ / $\sum_j$ $\xi_j$ , and relative selectivity between two products is simply the ratio of their two rates [ 2 ] . Selectivity is therefore a kinetic competition among simultaneous pathways, decided by which transition state a given surface site makes cheapest, not a property the catalyst “prefers.” Engineering selectivity means engineering which of several transition states sits lowest — through the identity of the metal, the geometry of exposed facets, a promoter atom that blocks one adsorption geometry, or a support that stabilizes one intermediate over another. A catalyst can be highly active and still commercially useless if it is not selective for the wanted product over faster side reactions.