I'm looking to forward requests from port 8003 on the remote machine to my localhost at port 8080
The OpenSSH command line given works just fine, but a few additional options make it complete:
Note that this will then forward any connections to 8003 to your local host on 8080; the connection is host-to-host. The -g option means anyone will be able to connect to that port on the remote machine. If you take out that option, only people using the machine directly will be able to use the tunnel.
The other options will put the tunnel into the background and keep it running without intervention.