It's the air injection passage & it runs from front to rear of the head connecting to the exhaust ports. If it is full of carbon then it's probable that there hasn't been any air flowing along it in a while. Have a look in the exhaust ports & you will likely see a hole in the port wall that connects to this drilling.

If the black crap is greasy, then it's probable that the engine was using a little oil [OK, a lot of oil] & the oil is now mixed in with the carbon that was blown in there by exhaust pressure when there was no longer any air flow from the air pump to help keep it out.

The air pump was connected to a fitting on the thermostat housing which screwed into the now-plugged hole, so I guess that the air pump was removed completely too.

The purpose of the whole thing is to mix air, which contains oxygen, with the still burning exhaust gasses in an attempt to completely burn any unburned hydrocarbons [fuel] & so remove them from the exhaust output. It worked reasonably well too, but EFI & cat converters solved many problems & it's not used any more in modern cars.
The only real downside is that this air pump drained a little power from the engine to run it & this is regarded as totally unnacceptable.