Most wall adapters consist of a step-down transformer and sometimes include a rectifier. They provide the lower voltage required by the device, and isolate it from the AC line to reduce the possiblity of electrical shock. Generally, they are sealed units and cannot be repaired.
However, the problem is often not in the sealed unit, but in the low-voltage cord that connects it to the device it powers. The wires inside the cords often break after repeated flexing, usually at the ends. If you need to replace a wall adapter, it is important that you get one with the right output.
You need to find out whether it puts out AC or DC, and what the voltage and current ratings are. While you can find "universal replacements" at some electronics retail outlets, these sometimes are not able to put out the right power that you need. If possible, try to obtain an exact replacement from the manufacturer.