A point worth making.
bitter_engineer says above "A method of creating prototype electronics board". And he's correct, that for most people, their exposure to wire wrapping will being when prototyping electronic circuits.
However, in some high reliability systems - such as TelCos - Wire Wrap is used for permanent connections. Why?
All forms of connection involve a physical joint. In most connection systems, this is effectively a spring holding two pieces of metal together. In the case of solder, a strong electrical bond is formed by the solder but the physical bond is weak. And in either case, there are only a few (2-4) actual points of contact between the two pieces of metal. (Even if two "flat" pieces of metal are touching, due to surface imperfections, there may still be not many true points of contact).
With Wire Wrapping, you wrap a wire round a thick pin with a square cross section. And you may wrap it, say, 6 times. This means that for each time the wire goes round the pin, it makes contact at each corner of the square. 24 points of contact.
Hence these are seen as very reliable and are often used for permanent connections.
Source: My employer makes hardware for TelCo's!