In short, powdered tea leaves. But which ones?
You start with your tea tree. For matcha there are certain cultivars that were developed specifically for their traits as they give off a better taste/aroma/mouth feel/flavour. These were made in Japan and so are best in Japanese soil, weather, and climate.
Next you want to shade these leaves for 4 weeks. This inhibits their growth, causing the tree to struggle, and in response it creates more chlorophyll in the attempt to capture more sunlight. This has the interesting affect of creating less catechins (polyphenols....remember this for later) and therefore less bitterness. The resulting leaves are harvested and processed. They are steamed in a vat and deveined by being blown through a cylinder at high speeds. Most importantly, they are not rolled. The leaves are left to dry without any rolling taking part. If they were rolled the flavour would change to something similar to a gyokuro, or so I suspect. The end leaf is called tencha. Dark green in colour, flat and thin, these leaves are soon to be ground into a fine powder.
From here you have two options when it comes to grinding down the tencha into powder. You can do it right and proper by stone grinding. This uses huge large rotating granite bricks that's slowly grind the tencha into matcha. This process is slow, but so is BBQ and god damn it if BBQ ribs aren't God's gift to mankind. Respect the grind, respect the grill.
The second option is to batter the tencha with numerous metal balls. Essentially you toss the tencha into a long spinning steel tube full of ball bearings which pulverize the tencha into matcha. The upside is that you can do a lot more volume (up to several kilograms) this way as opposed to stone grinding (which produces around 60-100g per hour).
The two methods make a world of difference. This is because of the friction involved. The slowly turning stone grinds generates less heat (from the friction) than the hundreds of steel bearings rubbing together. This heat burns the small matcha particles and degrades the flavour.
I must also mention here the importance of when the harvest occurred. Harvesting the leaves at different times of the year impacts the flavour, aroma, and colour of the matcha. If a tea bush was to be harvested throughout the year and the leaves processed the in the same method, you'd be certain to notice a difference in the end product.
This is the difference between ceremonial grade and kitchen grade.
Now you can get Matcha from sencha....it called funmatsucha (fu-n-ma-tsu-cha, 粉末茶). This term applies to any tea ground to a powder that is not tencha.
The upside is that funmatsucha is a lot cheaper as you don't have to spend time shading the leaves. If you've ever eaten "green tea ice cream" you've had this. It's simply a matter of cost. Why spend money on ceremonial grade matcha when it is just going to be mixed in with ice cream or flour. In this case you're aiming for that green tea flavour which will be very dominate in these powders.
An additional benefit is the polyphenols, yeah remember them from a few paragraphs ago? They are much higher in funmatsucha because there was no shading. So technically the health benefits are higher with funmatsucha....but it's also more bitter. Easy come, easy go.
Of course you can grind down any tea. I've been able to make oolong funmatsucha, black tea funmatsucha, and even houjicha funmatsucha. None were particularly delicious and I'd actually suggest you avoid these at all costs if you intend to just mix them with water and drink. Perhaps mixing these into a dough would make something worth eating.
In summary, matcha is powdered tea leaves. These leaves have been shaded and undergone a special processing method involving numerous steps to dry and devein the leaf. This leaf is called tencha and there are in fact entire factories devoted to processing this type of leaf.
Commonly matcha is described as powdered gyokuro. This is untrue. Gyokuro is a type of tea, yes, but it undergoes a different processing altogether. The confusion, I believe, comes from the fact that both tencha and gyokuro are shaded for several weeks. An easy mistake to make.