http://wiki.ffxiclopedia.org/Beastmen%27s_Seal http://wiki.ffxiclopedia.org/Category:BCNM
You use Beastman Seals to "purchase" an orb that lets you into a timed, instanced battlefield at various locations through Vana'diel. Typically they require 3 or 6 people, but there are some solo fights as well as alliance fights.
The drops that you may get from winning this battle (Often called BCNM or KSNM in case of Kindred Seals) are usually highly desirable items that you may use or sell. For examply, a Peacock Charm sells for over 2 million gil and is obtained from a BCNM. Kraken Club is another, and on my server sells for close to 40 million gil.
Some of the items have a rare/ex version of the item from a NM that is found in vanadiel, or a sellable version obtained from BCNMs. For example, Emporer Hairpin drops from a BCNM and is sellable, while an Empress hairpin froms from a NM is not sellabe/tradeable.
You'll want to hang onto those for doing a BCNM eventually and earning some money or items that you'll need/want.