In a cathode follower stage, which is analogous to an emitter follower in a solid state circuit, a resistor is placed in series with the cathode, the input is applied to the grid, the plate is connected to the usual high dc voltage (but directly, rather than through a resistor), and the output is taken from the cathode, rather than from the plate. Various other resistors are used for biasing.
A result of this is that the voltage gain is very close to 1 (actually, slightly less than 1). The fact that the cathode (output) voltage very closely follows the input (grid) voltage accounts for the name "cathode follower."
A second result is that the output impedance of the stage will be much lower than for a typical amplifier stage which provides its output from the plate. That enables the stage to, among other things, drive cables and loads which have significant capacitance, or relatively low impedance. The term "buffer" refers to the fact that the stage acts as a buffer between the amplifier stage, with its high output impedance, and whatever the buffer stage is driving.
In this case, the "cathode follower buffer" tubes are undoubtedly placed between the line amplifier stages and the outputs of the preamp, and so they are directly in the signal path. Intuitively I would expect the sonic effects of age-related degradation of their parameters to be somewhat less significant than for the line amplifier stages, but I don't have a feel for the degree to which that may be true.