LMS Algorithm: How to Define the Desired Signal
as the others have said you are best looking at practical examples of uses of LMS. once examples is noise cancellation. think of a system where we have two microphones, one mic is the source which contains speech and background noise. the other microphone will just contain noise. in this system we try to eliminate the noise from the speech. so the inputs to the LMS are our noise reference signal and the difference between the (speech + noise) - estimate of the noise, so in this case the LMS adapts to noise that appears at the source. 

Another example is echo cancellation. here you using your landline, which goes through a hybrid circuit, the signal from the far end x(n) is mixed with the near end signal u(n), so the signal going to far end is x + u + v = d, where v is noise. at the far end the person does not want to hear their own voice. so at the far end the user will have access to x(n), so inputs to LMS are x(n) and e(n) where e = d - y. in this case y is our output of LMS, used to remove the x from signal. 

in a comms system, as mentioned above the LMS is used to update the equaliser coeffs. in comms systems they use the training sequence (s[n]) which is known at both ends of the transmission system, this allows us to train the equaliser. this training sequence is used before speech transmision, and during speech transmission, and sometimes training is turned off completely if channel estimate is good. in this system the LMS has inputs r[n] (the recieved signal - the s[n] after passing through the channel), and e[n], which is from the s[n] - r[n], then you would update the equaliser coeffs f after doing f = f+mu*e*r.