A counterweight balances the weights on the other side of the clock mechanism (rather like when you try to balance kitchen scales to get an accurate measure of flour or sugar, etc.). This helps to keep the clock accurate. The stack (or pile) of old pennies (1/240th of an old British pound) provides the balance.

Counterweight helps the clock to function properly and stack of penny means a pile of pennies (it is fraction of british currency).

Ah! Old pennies. When I was young, there were 240 pennies to a pound. 12 pennies in a shilling. 20 shillings in a pound. We had coins worth thruppence (three pennies), and sixpence. We had ha'pennies too. (Half a penny). I got half a crown a week pocket money = 2 shillings and sixpence. A crown equalled 5 shillings. Expensive items were often sold in guineas (1 guinea = 1 pound and 1 shilling). Made the maths lesson at school a nightmare, of course.

A "stack" is a neat pile of things, one on top of another. We keep our dinner plates in a stack. The counterweight needs to be exactly the right weight. If it is too heavy, the clock will run a little fast. If it is too light, the clock will run a little slow. The counterweight is adjusted by adding very small weights to it. The surprise is that instead of using something specially made or extremely precise, it is adjusted by putting a stack of pennies on it. A penny is a British coin. The old English pennies were surprisingly big. The people in charge of Big Ben used pennies as convenient small weights. By the way: a nickel--the United States five-cent coin--happens to weigh almost exactly 5 grams. I don't know if that's just coincidence. Anyway, in the U.S. if you need a 5-gram weight for some reason, you can always find a few in your pocket. Here is another example of a humble, everyday object doing an important job in a grand piece of technology. The mirror of the Mount Palomar Observatory is 200 inches or 5.1 meters in diameter. For many years it was the largest in the world. It needs to be an extremely precise parabolic shape. When the telescope is turned to different elevations, the mirror would be slightly deformed by its own weight. To counter this, it is necessary to apply a very precise small force at various points on the back of the mirror. This is done by means of hundreds of spring scales, of the kind used by fishermen to weigh fish. P.S. Properly, Big Ben isn't the clock, it's the largest bell.