What they actually do
A mechanical watch movement has multiple pivots where moving parts (gears, balance, escape wheel) rotate against fixed bridges. At each pivot, friction would cause wear over time. Synthetic ruby (corundum) is hard, low-friction against steel, and chemically inert; placing a tiny ruby disc with a precision-drilled hole as the bearing surface around each pivot reduces friction by 5-10x compared to running steel directly against steel. Jewels also accept a thin oil film that further reduces friction.
Where they go
Standard jewel placement: balance pivots (top and bottom, plus the cap jewels = 4 jewels), escape wheel pivots (2), lever pivots (2), impulse pin / pallets (3), centre / third / fourth wheel pivots (6), barrel pivot (2), plus various automatic-winding wheels. A typical 25-jewel automatic accounts for all major friction points; chronograph movements add 4-6 jewels for chronograph-specific wheels (giving 27-31 total).
When more is and isn't more
Pre-1970s, jewel count was a quality marker, '17 jewels' was the threshold for a good watch. Modern movements have refined this; jewel count alone is not a quality indicator. A 25-jewel ETA 2824 has the same jewels as a 25-jewel Patek Cal. 324, but the rest of the movement (finishing, materials, regulation) is vastly different. Marketing inflation exists: some quartz watches advertise '7 jewels' that aren't structurally needed. A skilled watchmaker can tell jewel quality by where they're placed and how they're set.
Real ruby vs synthetic
All modern watch jewels are synthetic ruby: corundum (Al₂O₃) crystals grown via the Verneuil flame-fusion process or Czochralski method, then cut, drilled, and polished. Functionally identical to natural ruby but produced industrially in volume. Pierced jewels have a precise hole for the pivot; solid (cap) jewels sit flat above the pivot to limit endshake. Both types are essential; they work together.