Why piano strings break?

Imagine the sound of a whip snapping against an aluminum pie pan and you have some idea of the sound that occurs when a piano string breaks. It's startling for anyone standing nearby, but especially so if you're seated at the keyboard!
Realize that the thin steel strings are tensioned to an average of 150 pounds each and it's not hard to understand that they might break occasionally. Though they're engineered to withstand the high tension, three main factors can cause them to fail.

Corrosion
Over time, especially in a damp environment, piano strings can rust. The rust eats into the steel wire, causing weak spots which can then break during the stress of hard playing or simply during routine tuning. Replacement is the only cure for rusty strings.

Excessively hard playing
Bend any piece of metal far enough and often enough and it will break. That's exactly what happens to piano strings. Sustained hard playing, especially the rhythmic left hand style used in many churches, can drive the piano's hammers against the strings with such force that they eventually break. Regular maintenance to the hammers (see next) can reduce breakage, but very hard playing will still take its toll. One solution is to amplify the piano with a microphone and sound system so it can be played lighter and still produce adequate power.

Very hard and worn hammers
With use, the smooth rounded surface of a piano hammer wears flat. Then instead of striking the strings with the flexible, rounded shape of a rubber ball it smacks them with a flat, hard surface. This can over-stress the strings, especially if the hammers are also made of very hard felt. In this case it is critical that your piano technician keep your hammers properly shaped and their hardness adjusted through a process called voicing.