That is the pilot jet in Honda-speak, or the idle jet to most of us. The hole in the center of the lower end, near the O ring on the outside, is the actual jet. It is only 0.014" diameter, so it requires an unusually small probe. Honda says you should use an ultra-tiny gas torch cleaning probe, but standard sets of torch cleaners do not include a small enough one, and I have never been able to find one that small, so far anyway. I think most of us just buy a set of jet drill bits like these:
http://www.ebay.com.au/itm/Metric-I...DefaultDomain_15&hash=item5b11ddcfcd

Of course that makes more sense for those of us who face carburetor cleaning chores more or less regularly.

Remember that the Honda idle jet is just a plastic moulding, and it is quite difficult to deal with cleaning it without making the calibrated hole larger. The non-genuine ones (for Chinese Honda-copy engines, commonly called "chondas" here) have a brass bush lining the calibrated hole, and I personally prefer that.

Because you have no reason to suspect a problem with your idle mixture, I suggest you just remove the O ring, blow through the jet, squirt some carburetor cleaner through it, wash it in gasoline to remove the carburetor cleaner, which is quite unfriendly to plastics, put the O ring back on, and reinstall it. Do not allow carb cleaner to touch the O ring.