Synthesis whose goal is to reproduce, as accurately as possible, the sounds of accoustic instruments, or other non-electronically produced sounds. Imitative synthesis has been around for as long as synthesizers have existed; some performers take it as a challenge to produce synthesized sounds that people will mistake for conventional instruments. Others may use the synthesis as a way of understanding how an accoustic source produces its sound; by developing a similar synth sound, they may be able to deduce how the accoustic source works.
However, for others, their interests may be in using the synth to replace other instruments and the musicians who perform with those instruments. This is one reason that makes imitative synthesis controversial among synth performers and other musicians. When the Mellotron first appeared in the mid-1960s, this possibility made some people so nervous that the British musicians' union tried to get the instrument banned. Ironically, the Mellotron made a poor substitute for orchestral instruments, but its characteristic tonal qualities and its enabling the performer to play dense chords (something that individual orchestral sections don't usually do) led to it being used in a very different and not very imitative manner, and it is now a highly regard instrument in its own right.
But the music industry's interest in replacing musicians with synths continued. The analog synthesizers of the 1960s and '70s were not particularly facile at imitating accoustic instruments, but when Yamaha introduced the DX-7 FM-based synth in the early '80s, it turned out to be very capable at producing convincing imitations of piano and brass instruments. The DX-7 made imitative synthesis a force in the synth market, far outselling any synth ever made prior to that time. The DX-7 kicked off the whole arranger workstation market -- which led directly to the other reason that imitative synthesis has become controversial. When advancing technology made sample playback synths pre-loaded with accoustic instrument sounds inexpensive, it changed the direction of the whole synth market. These instruments were very capable of reproducing a large array of instrument sounds and replacing an array of musicians and performers.
Synthesists (as opposed to keyboard players who happen to play a synth) have found that since the early 1990s, imitative instruments have pushed many other types of synths out of the market. These imitative instruments usually have little or no capability to be programmed to create original sounds, and so they are of no interest to a synthesist. So, many synthesists resent the extent to which the imitative keyboards have taken over the market. As a result, imitative synthesis is in some disrepute, and some synthesists go so far as to avoid doing anything that might be described as imitative.