Reverse engineering was the process of studying a technology for the purpose of recreating it without the original design.
In the mirror universe in 2155, T'Pol advised Commander Jonathan Archer that the logical course of action upon capturing the USS Defiant was to return it to Starfleet for study, so they could reverse engineer its systems. (ENT: "In a Mirror, Darkly, Part II")
In 2259, Una Chin-Riley told Captain Christopher Pike that the pre-warp Kiley had collected enough data from the 2258 Battle near Xahea, which was less than one light year away rom Kiley 279 and must have had a hundred warp signs between Kelpien and Klingon ships, to reverse engineer a matter-antimatter reactor. This collected data led to the Kiley developing a warp bomb which was mistaken by the Federation for the development of warp drive. (SNW: "Strange New Worlds")