"Landscape" in its theoretical physics sense was introduced by Lee Smolin
in his popular book 1997 "The Life of the Cosmos". In 2003 the word was adopted by string theorists.
Intuitively the idea is that the Standard Model of particle physics depends on a couple of dozen or so parameters---numbers you have to plug in, like the masses of the electron and the quarks and the strengths of various interactions.
If these numbers were different the world would look different, with different chemical elements and different chemical and nuclear reactions. If they were TOO different there might be no stable atoms at all, just a soup of particles. And gravity could be stronger or weaker compared with the other forces, and so on. So by varying the numbers in the SM you get infinitely many VERSIONS OF PHYSICS.
Up into 1990s the dream of physicists was that a comprehensive theory, say with only ONE free parameter or none at all, would explain why the two dozen numbers had to be what they were. Then there would be no range of possibility, or at most a very trivial choice represented by the possible values of that single parameter input. String theorists in the 1990s shared this common aspiration, and hoped that string theory, when perfected, might uniquely determine the SM parameters. So they did not need the Landscape concept to describe the range of possible versions of physics, having other things to think about.
In 2003 a famous paper by four string theorists (Kachru, Kallosh, Linde, Trivedi) suggested that this goal of string theory would never be attained and that there would always be a huge range of possibility in string theory. The theory could not distinguish among something on the order of 10100
different ground states, or "vacuums". Later people estimated more, like 10500
or an infinite number of string vacua.
To many people there seemed no hope of finding a physical principle that would pick out the right one. At that point string theorists adopted the word "Landscape".
The word had already been given its physics-context definition in Smolin's popular 1997 book. Smolin says he chose the word "Landscape", for the range of possible versions of physics, to make the analogy with evolutionary biology, where the concept of a "Fitness Landscape" was well established. Think of all the different versions of an organism you can get by varying its genes (like the parameters of the SM in physics). Picture these possibilities laid out like some terrain and HEIGHT given by reproductive success, or fitness. Then natural selection will drive that species of organism to explore the landscape and find one or more "high-points" or fitness maxima.
In his 1994 paper, and later in the book, Smolin was investigating some possible mechanism by which the parameters of the Standard Model could be determined by a process analogous to EVOLUTION.
Some related discussion is in http://arxiv.org/hep-th/0407213
, "Scientific Alternatives to the Anthropic Principle"
---quotes from "Scientific Alternatives...---
Page 12 Footnote: It is perhaps worth mentioning that the word “landscape” was chosen in [8, 9] to make the transition to the concept of fitness landscape, well known in evolutionary theory, more transparent.
 L. Smolin, On the fate of black hole singularities and the parameters of the standard model
submitted to Physical Review D. gr-qc/9404011, CGPG-94/3-5 ;
Cosmology as a problem in critical phenomena
in the proceedings of the Guanajuato Conference on Complex systems and binary networks, (Springer,1995), eds. R. Lopez-Pena, R. Capovilla, R. Garcia-Pelayo, H. Waalebroeck and F. Zertuche. gr-qc/9505022;
Experimental Signatures of Quantum Gravity
in the Proceedings of the Fourth Drexel Conference on Quantum Nonintegrability, International Press, to appear, gr-qc/9503027.
 L. Smolin The Life of the Cosmos, 1997 from Oxford University Press (in the USA), Weidenfeld and Nicolson (in the United Kingdom) and Einaudi Editorici (in Italy.)