Best-Price Rule - Rule 14D-10
  
The best-price rule (also known by the far more boring designation of "rule 14D-10") is an SEC regulation that requires someone conducting a tender offer to give the same price for all the stock being bought.
A tender offer represents an attempt to purchase a lot of stock at once. Basically, the entity running the tender announces they are open to buying whatever stock they can get (up to whatever limit they impose). In the bad-old days before the best-price rule (it first appeared in 1968), buyers could offer sweetheart deals to certain sellers, buying certain shares for one price, while offering a lower price to the general public.
The best-price rule makes sure everyone gets the same amount for their stock.