(when used in this context) applies to a wireless network that is configured to allow access to any computer within range - provided it is equipped with a wireless network adapter. jazzypop is on the right track - whilst it is perfectly possible to run a mixed (Cat5 cable and wireless)network you'll still need to have a wireless access point or router. You can run a wireless access point off a hub, and then equip remote machines with wireless network adapters, or use a wireless router that will have conventional LAN ports for the cabled machines. The router will allow you to have the best of both worlds.
As far as your brother-in-law's security fears go, he's right up to a point. An ad hoc wireless network will, in theory, allow any Tom, Dick or Harriet to join your network, provided they:
1. Knew there was a network operating.
2. Were in range with a laptop/PC that had a wireless adapter.
3. Could be bothered in the first place.
In the real world it's not a problem with a home network - the range is never good enough for a crowd of illicit surfers to gather in the street.