as an example, imagine a time-varying comm. channel, first in a small time u send the known data and reciever will calculate the coefficients for its equalizer according to the desired output that transmitter already has sent. and then it will use the adapted equalizer to equalize the channel for the unknown recieved signal.
so u have used the desired output to specify the adaptive equalizer coefficients and after that to equalize the channel with unknown output.
and so on for adaptive signal processing and adaptive noise cancellation and...
take a look at an "adaptive filters " book like that of Haykin.
cheers