What do Frozen Synapse's "Focus on Zone" commands do, and how do I use them?

The commands are grayed out because you haven't defined any zones yet. Use the hotkey 't' to create them. Put the cursor at a corner of where you want to start the zone, hold t, and drag to create the zone, letting go of t when you're done.

Now, when you have a unit selected, you can rightclick the zone and use focus/ignore on that zone.

You can create multiple zones, but I'm not sure how overlapping zones work.

As for the commands themselves: Focus on Zone: the unit will only target enemies within that zone, ignoring enemies outside of it. If there's no one in the zone, but someone out, I think they will ignore that enemy, even if its the only one (Not 100% sure on this). They continue to focus this zone until you cancel the command.

Ignore Zone: the unit will ignore any enemies within the zone. Pretty much the opposite of Focus on zone. This is helpful if you don't want your MG shooting at a far enemy emplacement (ie behind a window), but instead targeting whatever might be in front or around of it (since you'll lose the battle against that far window if you're walking up to your new firing position).

One final thing, I haven't tested this and don't know if its true, but just something to be aware of: I've heard that once you create a zone, your opponent will be able to see it next turn. I'll try to play a friend and try that out tonight.