In as simple of a term projection design can be signified as both a subject and a question. In as much as one can answer the 5W's of investigation (What, Who, Where, When, Why) as well as the definition of a noun (Person, place, thing, or idea) as projected imagery and the manipulation of it allows for the solution to the questions posed by the text. It is easy to assume that this could be considered the oldest use of projections, but in fact that fails to take into account the Phantasmogoria's of the 18th and 19th century, the experimentation of cinema, and magic lanterns by magicians in the late 19th century, and light shows from artist like Thomas Wilfred in the early 20th century. However, in the mid 20th century this was the main use of projection design in commercial American Theatre with the use of slide projectors. In that format in it's simplest form projections can provide the opportunity to contextualize that information to define the space.
It can be as simple as projecting the words 'noon,'
Designation of time from 'columbinus' 2012
to what can be defined as a scenic backdrop whether still or moving. The dynamics of which can be explored either in the defining of a space (ie the place itself) or the feeling of the space. Such as moving branches on a window, or scrolling images on a idle computer.
Dead moving branches on voile windows in 'The Stone Witch' 2016
The Devil's Ball in 'The Master and Margarita' 2014
Faustus after the deal is finished, with idle computers in the background 'The Life and Death of Doctor Faustus' 2015
In short contextual projections simply places the character and audience with the world defining time and place. Defining the space is an expensive enterprise to invest in when dealing with projections, as the first priority of this path of representation is believably. More plainly, does this world mesh with the world of the play that has been also defined by the scenery, costumes as well as the other design elements. Does it communicate the dimensions of the space, does it shift with the rhythms of the text, can it disappear are all questions that must be take into consideration, is equipment powerful/sofisticaed enough to acheive these things. In one sense it can be defined partially as a realistic rendering of a fictitious reality on stage. In another way it is a great way to set up an expectation from the audience providing the illusion of expectation to the surprise of a change to that same space.