Simply put, the cable spins a magnet, the magnet rides inside a small steel bell shaped part that's connected to the needle on the face. With your engine running the cable spins the magnet which couples to the bell via magnetic field, raising the needle to indicate engine RPM.
Its a brilliantly 20th century (or earlier) design, all mechanical and generally reliable.
Be careful not to use solvents that can get onto the tach face, that paint damages easily.
On mine I cleaned out the old lube with brake cleaner and re-oiled with 3in1 oil on a toothpick. Then I had to JB weld the part the cable threads onto back in place. This part contains the bearings, shaft and magnet assembly so alignment is important or the magnet rubs the bell. Mine had worn through the bell in one spot, but its good now after no less than 2 layers of JB which are squashed in place by the gauge cup.
Mine came out pretty ugly but it works and I learned a lot.
Hope it helps, YouTube is your friend.