Why 'grandfather clock'? The proper term is longcase clock. The popular name comes from Henry Clay Work's song 'My Grandfather's Clock' (1876), about a clock that stopped when its owner died. The song was hugely popular and gave the name to the whole type. Smaller versions came to be called 'grandmother' clocks, and very small ones 'granddaughter' clocks, but these are informal names.
Why the tall case? It is there to hold a long pendulum and to give the weights room to fall. The anchor escapement, introduced in England around 1670, allowed a long pendulum with a small swing. A pendulum of about 39 inches (a 'seconds pendulum') takes one second per swing, which gives the familiar slow tick.
Power comes from the weights. One, two or three heavy weights hang on cables or chains. As they slowly fall they turn the drums of the movement. Winding them back up, with a crank key or by pulling the chain, restores the power. Many clocks run for eight days on a full wind, and thirty-hour clocks need daily winding.
Timekeeping comes from the pendulum. The escapement lets the gear train advance one tooth each swing, and gives the pendulum a small push to keep it going. The length of the pendulum sets the rate. Raising the bob with its rating nut makes the clock faster, and lowering it makes it slower.
The chimes and strike: separate trains, each with its own weight, run the hour strike and, in chiming clocks, the quarter chimes such as Westminster, Whittington or St Michael. Levers on the going train release them at the right moments.
Common reasons a grandfather clock stops include a case that is not level ('out of beat', heard as an uneven tick), weights hung on the wrong side (they are often different weights), and old, dried oil. Leveling the case restores the beat. Anything more needs a clockmaker.