FAPP is an abbervation of "For All Practical Purposes", a pragmatic approach toward the problem of incompleteness of every scientific theory and the usage of asymptotical approximations.
Usually, when a physicist makes an approximation - which can't be justified on rigorous grounds - he tends to justify it by saying that the results obtained are good for all practical purposes (FAPP), meaning that they agree with our experience and approximation errors cannot be detected in practical measurements (for instance, if the error is smaller than the measurement resolution).
FAPP theories are incomplete or lackly-based theories that nevertheless have very high agreement with experiments and tend to be very useful for all practical purposes.
See also