Water heater elements typically must be replaced if they break. While those with specialty tools and experience with electrical work might be able to fix a broken heating element, the relatively low cost of replacement generally dissuades people from doing so.
Water heater elements are fairly simple devices. A wire runs through them and uses its inherent resistance to generate heat, and the casing around the wiring radiates the heat into the water. If the wire itself breaks, it is impractical to run a new wire through the casing. If the casing itself cracks, there is no easy way to repair it, and water may damage the wiring; however, replacing a broken heating element is a straightforward process.