Wires are strips of metal often covered by an insulator. They are meant to direct the flow of electricity from one component to another. The ends of wires may be directly attached to components or use connectors to make some sort of attachment.
Solid wire only has one piece per cable, and thicker solid wire can hold a bend. Some wires are so small that they can only be produced as a solid wire. Most solid wires used in vehicles are small.
Stranded wire has multiple pieces in it, which makes it easier to work with and allows chemicals (such as solder, used to hold wire to other components) to seep in to the ends. Some wires are so thick that they must be made stranded, or else they would be rigid or would bend with too much difficulty. Because of their flexibility, stranded wire the most common type found under the hood.
The most common conductive material used in wires is copper. Sometimes aluminum is used, and there are a few other types of metal that are sometimes used for special applications.
Insulation is applied to wires so that they don't short out any time they touch another metal object. The insulation can be found in many different colors, including colors with a stripe of another color on them. The colors are often used to indicate different components and polarities, such as red for positive and black for negative on battery cables. Sometimes wires heading to a left component and right component will have the same color with a different color stripe.
Wire connectors are typically found at the ends of wires to give them some sort of connection, such as a terminal or ring. Terminals are a common male or female connection. Ring terminals allow for a bolts or screws to hold down the connection, as long as they are conductive (nylon or plastic screws won't work in this situation) and make contact with where the electricity needs to go.
Soldering is often the preferred method for attaching two pieces of stranded wire. It involved melting a metal solder with a relatively low melting point, then letting it cool down so that it hardens, providing a solid connection both physically and electrically. The following video provides some examples, and including showing some examples of flaws.
Shown here are a few examples of solder attempts, with comments about how some could have been done better.