It was designed to supersede and replace duotronics, also designed by Daystrom, then in use throughout Starfleet. It utilized very sophisticated technology, probably similar to the Human neural network. The goal of the system was to allow starships to run entirely without the need for a crew, controlled only by their multitronic computers.
Five multronic computers were constructed before the project was abandoned. M-1 through M-4 were total failures. M-5 was installed aboard the USS Enterprise in 2267. Its test was also a failure, resulting in the destruction of the Woden, an unmanned robot ship, and the USS Excalibur , a Constitution-class heavy cruiser. (TOS: "The Ultimate Computer")
Multitronics were a part of the EMH Mark I holomatrix. When The Doctor's memory pathways became degraded in 2373, Kes had to prepare his multitronic paths before an overlay could be made from the diagnostic program. Most of The Doctor's memories remained intact after the process. (VOY: "The Swarm")
Multitronic devices were also still in use in 2375 when Doctor Julian Bashir and Miles O'Brien used a multitronic engrammatic interpreter while linking their minds to that of Section 31 operative Luther Sloan. (DS9: "Extreme Measures")