NAT is usually a one-way translation. You probably have one outside (public) IP address, and many inside (private) IP addresses. If traffic comes to your outside address, absent any other information, the NAT cannot determine to which inside address it should forward the traffic.
For some things, you can set up port forwarding, e.g, you will forward any traffic destined to your outside address and port 80 to a web server.
When a host inside your LAN initiates a connection to an outside host (e.g. your web browser wants to connect to a web server), it will use a random, ethereal port as the source port. For traffic to come back from the outside to this ethereal port, the NAT needs to record the port in its translation table. When traffic comes back from the outside host, destined for that ethereal port, the NAT knows to send it to the inside host address and ethereal port. This is port triggering.
With NAT, you either need to manually configure port forwarding, or your NAT needs to do port triggering. Most NAT routers will automatically do port triggering without specific configuration. Some will let you change some parameters, e.g. how long it should keep the port triggering enabled without any traffic.