The nerve conduction test is simply a test where the doctors use some electrical measurements to see how strongly a nerve reacts, and how fast the impulse travels across the nerve.
So, if a signal is weak in the nerve, then they can surmise that the nerve has some type of damage to it.
If the signal is considerably slower than expected to travel through the nerve, then again, they can surmise that there is something affecting the signal conduction through the nerve.
In your case, they may be wanting to look for two things, which are carpal tunnel syndrome and ulnar neuropathy.
These can cause pain and/or numbness in the forearm, wrist, and hand areas.
Of course, the test will help to guide your doctors to a diagnosis, then the actual treatment will depend on what they find.