Tannin is found in the stems, seeds and skins of many fruits including apples. It is a natural preservative and so critically influences the ageing process of cider (as well as wine, leather and other products). High tannin ciders have a longer life than low tannin ones. Which is good, except that tannins are really only detectable to humans by taste. Tannins are bitter and/or astrigent; you taste the bitterness and the astringency creates a dry feeling in the cheeks. So the correct level of tannin is key to the balance of your cider. Get it wrong and your cider will taste too sweet (and go off quickly) or be too bitter (and last for ever to remind you...)
Different cider apple trees produce fruit with different tannin levels. Bramley apples (widely used commercially) have tiny amounts of tannin (about one fifth of what is required), while apples such as Sandford Jersey can have twelve times as much tannin as a Bramley (more than double what is needed in a medium cider).
As well as being astringent and bitter, tannins oxidise when the apples are milled giving your cider a deeper orange colour.
The second important property of a cider apple is acidity. This is much easier to explain than tannin. Everyone knows what a lemon tastes like. It is sharp, and here sharp equals acid. Apart from imparting a sharp edge to a good cider, acidity is also important in ensuring good fermentation. If acidity is too low your brew will be susceptible to fermentation diseases. If it is too acid, the fermentation will be fine, but the cider will make you wince. Good old Bramleys are hugely acidic - more than double what is needed, while an apple like Yarlington Mill has half the acidity you need for a good fermentation.
Kingston Black is almost perfectly balanced, but is very canker prone, so our advice is to never put all your cider eggs in one basket. Much better to choose a selection of trees that produce fruit you can blend to make your perfect cider(s)