There is a very good page on STO Wiki that explains this....
http://www.stowiki.org/Badge
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Badges of Exploration are a form of non-tradeable in-game currency given as a reward for completing exploration missions. There are five orders of badges, each corresponding to which Mark level of items you can purchase from certain requisition officers, such as the officers located in the Starship Requisition area within Earth Spacedock or the shipyard at The Great Hall of Qo'noS (see the vendors section for a list of NPCs to trade in your badges to).
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