What is a taxi medallion?

In the U.S.

THE MEDALLION SYSTEM'S PRIMARY FEATURES
The medallion system dates from a Depression-era city law designed to address an overabundance of taxis that depressed driver earnings and congested city streets. After rejecting the recommendations of a series of mayoral panels studying taxi problems, the city Board of Aldermen in 1937 adopted the Haas Act, which slapped a moratorium on the issuance of any more taxicab licenses. Over the next several years, the number of cabs, which had peaked at 21,000 in 1931, fell from 13,500 in 1937 to the present number of 11,787 because the licenses of taxi owners leaving the industry were not reissued.11

While the vehicle cap is its most famous provision, the Haas Act had other significant and enduring features. It provided for the automatic renewal of vehicle licenses and allowed for the transfer of licenses between owners, conditioned only on City approval of the new owners' qualifications. This transferability provision was vital to the subsequent establishment of license values. The Act also erected a wall between fleet-owned taxi licenses and individually owned licenses, a clause intended to ensure the survival of owner-drivers.

The Haas Act also created a mechanism under which the city could issue additional vehicle licenses after a deliberative administrative process.12 This provision, which some critics of the Act have ignored,13 was never exercised and was removed in a 1971 rewrite of the law. When the City failed to expand the taxi industry despite post-World War II economic growth, taxicab licenses developed a trading value in the open market. After four decades of often-explosive increases, individually-owned licenses now trade at $155,000 and fleet licenses at $220,000 each.

From:
http://www.schallerconsult.com/taxi/taxi2.htm#primary

If this is a US question, I can't be a 100% sure (being a Brit) but if it's the same as a UK Taxi plate, then this is the proof the the vehicle (and diver) have been licensed as a taxi-cab service. To qualify to work as a taxi (or cab), the vehicle not only needs to have a valid MOT and insurance, but also an additional 'safety MOT' to prove its viable as a taxi.This needs to be re-tested and approved regularly (just as a vehicle's MOT is). As a passenger, you know that the taxi you've just stepped into is legal because the successful certificate of license is displayed in the cab. In the UK, this is a small metal 'plate'. I don't know if the US cab actually displays a medal instead, or if that is just the name given to another shaped plate or certificate instead.

Go to www.beataxidriver.com