The company publishes a range, say $38 to $44, and shareholders submit the lowest price at which they will sell. The company works up from the bottom until it has bought the shares it wants; that level becomes the clearing price and everyone accepted receives it, even those who asked for less.
Holders who name a price above the clearing price keep their shares. Naming a price at the bottom guarantees participation but gives up nothing, since the clearing price applies anyway.
Example: a company seeks 15M shares between $38 and $44. Enough shares are offered at or below $41 to fill the order, so $41 is the clearing price and a holder who tendered at $39 still receives $41.
Related: tender-offer, share-buyback, treasury-stock, outstanding-shares