In general there are two types of wires:
The first type of wire is called solid wire [pic 2], and this consists of a solid piece of copper or aluminum wrapped up in some insulation. Solid wire is cheap to make and sell, and that's why they it's used for wiring houses. It has a downfall however, and that downfall is that it is stiff and fragile. It is stiff because it's a large strand of metal, and it is fragile due to metal fatigue. Simply put, if you bend it enough it'll break.
The second type of wire is called stranded wire [pic 3], and this type is used when a the conductor needs to be flexible. Inside stranded wire are small strands of metal. These strands are easier to flex and can withstand more bending than a solid wire, so this type of wire is used in cables and computers. The more strands a wire contains, the bendy-er it is. The flexibility of stranded wire can vary from pretty stiff to wet noodle, depending on the the wire's insulation and the number of strands. Although rather uncommon, silicone insulation is the most flexible.