How do two computers connect to same external address through NAT?

Question

If I have two internal computers connecting to the same external IP address through a NAT router, how is the router able to get the traffic to the correct internal computer?

Answer 1

Already good answers are provided, but here is another example:

    HOST A addr         HOST B addr
    10.1.0.2:4040       10.1.0.3:4040
-----------------------------------------
NAT 200.50.50.28:4040   200.50.50.28:4041 (what external host sees)

200.50.50.28 is router's global (internet) IP.

Every port number is unique in the NAT table. And of course the router does all the dirty job of modifying the source and destination addresses transparently.