The two LANs are protected from the Internet by firewalls, so a user on LAN A can't get to LAN B, at least not without making a hole in the firewall that could be a security hole.
The VPN puts routable connections inside the firewalls, so that traffic between the LANs travels within a protected tunnel.
Each of these deserve their own presentation. IPSec is the preferred solution, but can be difficult to configure. CIPE is a good solution. PPTP is also a good solution, but the most prevalent implementation lacks quality and the security it is supposed to provide. This presentation focuses on SSH and PPP.
If you are not using a secure mechanism for connecting to your home system across the Internet, you should! SSH is freely available and provides a good level of security.
The above is the performance between a 400MHz PII and a 533 MHz VIA Mini-ITX system. When run between the 400 MHz system and an Athlon 1800 system, the time for the tranfer was about half (i.e., 3 seconds for no VPN, and 30 for the VPN), but instead of CPU load on the sender being ~50%, it was 99%.
In this example, a firewall appliance is used to forward the SSH port to a system on the LAN that will accept the SSH connection and act as one end of the tunnel. Note that unless this node is configured as the router for the external subnet for the wireless LAN, this node should be acting as a NAT, thus all traffic coming through the tunnel will appear to all other systems to be coming from System X.