Material - Obviously the material used when making wire needs to be a good conductor of electricity, or more simply allow electricity to pass as unrestricted as possible. Due to this single restraint, metal naturally becomes the ideal wire material because most metals have very good conductivity, are readily available and are also relatively inexpensive. Aluminum, copper, nickel and certain metallic alloys such as steel make up the majority of what is used when making electrical wire. There are other metals such as silver and gold that are very good conductors but are much too expensive when used in the scope necessary to meet demand.
Solid vs. Stranded Wire - Solid wire is made up of a single piece of metal wire. Stranded wire is comprised of multiple (at least 7 strands) smaller diameters of wire that are bunched together to reach the necessary gauge. Both types of wire are fundamentally the same and are used to pass electricity from one point to another but each has separate advantages when used in certain circumstances. Solid wire is cheaper but also is far more rigid than stranded wiring. Stranded wire is flexible and provides more conductivity but again is more expensive.
Gauge - When discussing gauge of wire there is a helpful analogy for understanding importantance. Think of the wire being used as a garden hose and the electricity passing through the wire as water. When you use a hose with a larger diameter you can push more water through the hose at any one time when compared with the smaller hose. This same principle holds true to the flow of electricity through wire. The larger gauge wire you use the more current or amperage you can pass through the wire at any one time. Physical constraints of the size wire you are using can have serious repercussions if not applied correctly ie. Forcing excessive electrical current through the wrong size "hose" can cause extreme heat or fire and/or short out your circuit with possibility of electrocution.
Insulation - Most wire is covered by a variety of different materials and this process is referred to as insulating or jacketing the wire. Wire insulation is always non-conductive and typically is comprised of glass, ceramic, rubber, plastic or a large variety of plastic polymers. Think of wire insulation as a protective blanket around the outside of metal wire itself. This protective coating ensures that the electrical current flowing through the center of the wire can only flow from one end to the other and not out of the middle into something else (another conductor, for example a piece of wire or your hand) near it. Insulation is important not only because it keeps the electricity from escaping it also serves an important secondary task by keeping other detrimental elements like moisture out of the wiring. Lastly, insulating the wire protects the internal metal from wear and prolongs the wire's lifespan.
Length - The length of wire is varied in every application it is used, thus length isn't a manufacturer variable but is still important for the resistance properties it exhibits. The longer the wire the more resistance the electricity flowing through that wire will experience. This is important because you may expect a certain amount of electricity to pass in theory but that amount of power will be less due to resistance inefficiencies.