Cone wrenches are thin open-ended metric wrenches designed to fit the narrow nuts found on hub axels. A set of cone wrenches will normally come with sizes ranging from 11mm to 19mm. If you are only going to be working on one or two bikes, you may find it worthwhile to figure out what size cone wrenches will be essential to you and only buy those. Most hubs (I tend to find) take a 13 -15mm combo to service, find out what wrenches you need. Most major tool makers sell cone wrenches as a set and individually. If you are buying tools for the first time, you will want to make sure that the kit you buy includes the wrenches you need the most. Alternatives to cone wrenches include the trusty crescent wrench also known as an adjustable wrench or your neighbors open ended wrenches will do the trick most of the time. Note that these wrenches are often too thick to fit axel cones hence the existence of cone wrenches.
P.S. Your 15mm cone wrench is not a pedal wrench, I pity the foo.