There are two kinds of wire for the transmission of electrical power or signals: solid or stranded. Solid wire is made of a single thin, flexible conductor, almost always circular in cross section and usually made of copper or aluminum. Stranded wire is similar to rope or string in that it is one wire made of many fine strands of wire twisted together like a rope. Both are measured on the same American Wire Gauge or metric standard of thickness and have the same current-carrying capacity for their thickness.
The advantage of stranded wire is mostly in flexibility. Solid wire, especially thicker wire, can be very stiff and difficult to bend or fish through conduit. Furthermore, the more often solid wire is bent the more likely it is to break. Stranded wire can be bent much more easily and withstands repeated bending with minimal risk of breaking because the stresses on each individual thin strand are much smaller. For use in locations where the wire may be bent or flexed often, or the wire removed and reconnected frequently, stranded wire stands up to the abuse better. This is why power cords in household appliances are made of stranded wire. Ethernet patch cables are also available stranded for applications where they may be moved often.
On the other hand, when solid wire is bent, it stays where it is put much better than stranded wire. This may or may not be a good thing depending on the particular application. Furthermore solid wire is easier to set into screw terminals because there is no risk of stray strands splaying out from the connection and causing an accidental short circuit with the next connection over (although tinning the wire ends eliminates this problem). Solid wire is also easier to strip the insulation from, because you don't have to worry about accidentally clipping off a few of the strands by accident.
Which brings us to the single biggest mistake that people make with stranded wire. The ability of a wire to conduct electric current safely is directly related to the diameter of the wire, but people who don't understand how important this is often trim stranded wire down by cutting off half the strands in order to get it to fit in a terminal that is too small for it, or to fit more than one wire into the terminal. This seriously degrades the ability of the wire to efficiently and safely transmit electric current and in the worst case could result in breakdown of the wire insulation and an electrical fire. Stranded wire is intended to be a certain thickness, and care should be taken to ensure the strands are intact.