"Make Service Inactive"

For your setup, I'd do several things:

1. Turn airport off in System Preferences > Network > highlight wifi on left and turn it off. You don't need it with direct connect.

2. Make sure you're not sharing anything in System Preferences > Sharing > uncheck everything in the left panel.

3. Turn on the firewall. System Preferences > security > Firewall tab > start.

Regards,
Captfred

If it's off then you're invisible to others

I'm not sure where you see inactive but I'd just turn it off. Don't delete the service.

Regards

Edit: What could happen is that you inadvertently connect to a neighbor's wifi service.

Message was edited by: captfred

For your purposes I don't think it really matters whether you turn it off in the menu or make it inactive in preferences. You could make it inactive just because you'll never use it. Technically, if it is "off" then scripts or other software can be programmed to turn WiFi power back on. (I have scripts that do that when automating a Location switch on my laptop.) If you make it "inactive," then when software goes to turn it on, it simply isn't there and might produce an error like "interface not found," but of course you probably won't be running anything that wants access to WiFi.

beckyk1 wrote:
I have an iMac with a direct connection to my cable modem (ie no router), using an Ethernet cable. Should I set Airport service to inactive (the gear thingy)? If I do not, does that mean I will be "discoverable"?

Normally, even if your AirPort was on, your iMac wouldn't been seen by your neighbors unless you had some type of sharing on, or if they were technically advanced and specifically running software that looks for wireless client packets.

Now, about discoverability and sharing...if you are on cable with no router, I have heard that some cable systems wire up a neighborhood such that it's as if they were all in the same office, which means sometimes you can see computers show up which are in houses down the street. If your cable system works this way, then even if you are wired, you need to have your firewall on, and stealth mode on, and you need to be aware of what you are sharing. By that I mean, watch out for iTunes sharing and iPhoto album sharing. If they are on, your music and photo albums might be being published over the local network. If all Mac sharing possibilities are turned off, and you are firewalled and stealthed, you should be non-discoverable...

...watch out for Bluetooth too, though. If Bluetooth is on and Discoverable, somebody within range of the Bluetooth signal could locate your Mac.