These small closed cylinders of soft metal are crimped over the inner cable end to prevent fraying/unraveling of the cable. This is more important than it sounds at first,cables last longer and don't damage clothing as a fraying cable can. It may even stop a small but very annoying puncture wound on your calf. Sometimes these are provided with replacement cables - they are always fitted to new bikes.
A better solution is to use a soldering iron and some soft solder to the same end- simply heating the cable , "wicking" in some solder and then trimming for neatness. With this method there is no possibility of it going astray- as crimp on ends can and do.
A very cheap and effective solution is to use an old spoke nipple. The nipple is slid over the end of the cable and crimped on with a sturdy pair of pliers. Some pliers have a crimping area behind the pivot which works vey well.