Linear ("analog", continuous) as distinguished from digital ("binary", two-state). Some people have used otherwise binary/digital ICs (notably inverters) as linear/analog amplifiers for circuit applications where distortion and noise is not important. Of course all integrated circuits are linear/analog INSIDE. But "digital" chips are designed and optimized for operation at the "rails" where a binary zero is represented by a lower voltage and binary one is represented by a higher voltage. And there are some integrated circuits that are BOTH linear and digital, like comparators and analog-to-digital converters, and digital-to-analog converters.
Monolithic as in "one-piece". Before the development of the monolithic integrated circuit, Jack Kilby (Texas Instruments) had devised "integrated circuit" technology with separate little bits of substrate for different components, and wire-bonded together. In the case of Kilby, he was working in Germanium at TI, and meanwhile, out in California, Bob Noyce (Fairchild then Intel) was doing parallel development in Silicon.