Port Address Translation is a function of Network Address Translation. With NAT, a single external address is used and all outbound traffic is translated to that address for the source, so that the internal IP's of the machines are hidden. When the response comes back, the firewall or router translates the destination IP back to the internal computer's IP and sends it on. The firewall or router has to keep track of which ports the traffic is going in and out on, along with which router started a connection to which remote address, otherwise multiple computers couldn't work through it.
PAT allows port forwarding, where the firewall is configured to forward inbound connections to a certain IP on the internal network, based on which port the connection is sent to. This allows a server to be run on the network using only the external NAT IP, and stops any unwanted traffic from getting past the firewall. PAT isn't used unless NAT is already configured.
Why are you using a PIX exactly? A Linksys router works perfectly fine for most uses, unless you're trying to run a business and need high reliability and extra features.
To configure the port forwarding, you'll just have to find the configuration options for it. The manual for the PIX should have a section dedicated to this, and Cisco's technical support is very responsive and helpful, as is their website. I'm not sure whether the PIX has an easy interface for setting things up, or if it uses the normal Cisco text configuration file, which uses a lot of statements like this:
ip nat inside source static tcp 192.168.0.5 80 171.68.1.1 80 extendable
to create port forwarding behind NAT.