The question is similar to asking, "What are dollars?". The answer is similarly long and complex.

The Greek monetary system before the time that coinage was invented was based on crudely shaped sticks of cast iron. There were six obols to a drachm - an "obol" being an iron stick and "drachm" meaning literally "handful", as many iron sticks as you could hold in one hand. As you can imagine, the locals found handling tiny pieces of silver much more convenient than passing around awkward and heavy iron sticks. But they retained the monetary system: six obols to a drachm.
You can't make a very large coin from one drachm's worth of silver, so before long they found it necessary to make multiple-drachm coins. Didrachms (2), tetradrachms (4) and even octadrachms (8) and dekadrachms (10) were made at various stages in Greek history, but by far the most popular denomination as a trade coinage was the tetradrachm - it was "just the right size". Athens set the standard, literally, with their famous "owl" tetradrachms: their weight and fineness, the "Attic standard", was later adopted by Alexander the Great and his successors as the standard coins in their respective kingdoms. Cities throughout the Greek world, from Sicily to India, were striking tetradrachms.
Tetradrachms lasted longest in Egypt, where the Ptolemaic dynasty of Greek Pharaohs ruled until the Roman conquest. The Romans made Egypt the personal property of the Emperor, and gave it a closed economic system with its own coinage, based on the tetradrachm. By this time the tetradrachm had fallen in weight and silver content so that one tetradrachm had about as much silver in it as a Roman denarius, though the tetradrachm was larger and more debased. 1 tetradrachm approximately = 1 denarius was the exchange rate for the next three centuries.
As the Roman denarius itself became debased through the second and third centuries AD, so too did the Egyptian tetradrachm, until it, like the denarius, had no detectable silver in it at all. The Romano-Egyptian tetradrachm was finally abolished during the monetary reforms of Diocletian, circa 300 AD.
Finally, a word on pronunciation. The "ch" in "drachm" is in Greek the letter
chi, which has no direct equivalent in English; the German and Scots
ch sound is a closer match. The closest we have to pronouncing it right is the "ch" in "Christ", but NOT the "ch" in "church"; "tetradrakkem" is how I've usually heard it pronounced, and how I've usually pronounced it myself. The old pre-metric English unit of weight, the "dram", derives its name from the drachm, so pronouncing it "tetradram" wouldn't be too wrong, either.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis