The other end is attached to the sense line that comes from the Alternator. Its use is to remove noise/transients and shunt them to ground. Think of it as a noise filter. Without it, and all the others (alt, coil, etc), your radio would buzz with the frequency of the alternator/engine rpm.
Testing is not very easy without special equipment. If you have a lot of noise on your 12VDC line, you may want to replace these parts. Not a high failure item, though.