Welcome to FT charlesrhona.^
Each letter ("class") represents a certain amount of seats ("inventory") in each cabin. Each letter also has a fare attached to it. So the letters are used to manage inventory and prices.
I will attempt to explain what they mean with an example.
The first class cabin has three classes which can be sold. They are F, A and Z. F is always associated with the highest fares and A fares are always lower than F. Out of 14 seats in the nose of a 747 BA's yield management system will calculate how many seats in each class to make available for sale.
When the flights open 360 days in advance all 14 seats will be available for sale in F (although sometimes F availability may be less than 14 if the country where the fare is being quoted in is less expensive than the point of sale at the other end of the route - fares are available in both directions).
14 seats may be available in A if the flight is not expected to be constrained. But the more demand anticipated the more seats will be protected for F. Similarly Z (mileage redemption - fuel surcharge revenue only) seats will probably only be available for sale if all the seats are not expected to sell for money. BA will generally prefer to sell a seat for money than for miles.
So the number of seats available can be modelled as F >= A >= Z. Z is said to be nested in A and A is said to be nested in F.
Similarly for Club J >= C >= D >= R >= I >= U where U is the mileage redemption class.
For WTP W >= E >= T >=P where P is the mileage redemption class.
WT I am not sure about.
For the fares available for sale. F > A, J > C > D > R > I and W > E > T.
It is not always true that A > J, I > W and T > Y.