My wife's elbow is causing her some pain, right at the pointy end of it. It hurts when the point touches anything hard. What could be the cause?

Olecranon Bursitis. Sounds like she may have a little elbow bursitis. It is treated conservatively with padded protection of the olecranon. If it is swollen, it can be aspirated and then injected with a small amount of steroid. Either way, you should likely see a physician to get hands on.
Is it swollen? If it is swollen, the most likely explanation is olecranon bursitis. This is an inflammation, or much less commonly an infection, of a "sac" that crosses the elbow joint. It most commonly becomes inflamed from overuse or repeated contact with a hard surface.