Projection mapping is exactly as it says on the tin it is simply deciding on the place on which you want to project such as which part of the wall you wish to project on.
Complex 2D projection is were you project an image onto a complex shape as seen in the photo to do this yo would create a too scale 3D assembly of the building / object you wish to project onto then use a uv un-wrapper to get the perfect net of the building / object. the net is then used to design the image so that it fits perfectly when projected.
Other forms of projection include holographic projection (were the image is projected from multiple angles onto a sheet of water vapor.) And interactive projection where the image and a person are either well timed or motion tracking technology recreates the persons movement in a physics engine so that ‘soft body’ and ‘ridged body’ enabled particles will appear to interact with a performer.
projection can be taken further with careful planning and sophisticated technology so that instead of projecting on static objects you can project on organic mobile objects and people.
Here are some videos of projection mapping in action:
And when you swap the walls and projectors around:
Wikipedias definition of Projection mapping is:
Projection mapping, also known as video mapping and spatial augmented reality, is a projection technology used to turn objects, often irregularly shaped, into a display surface for video projection. These objects may be complex industrial landscapes, such as buildings, small indoor objects or theatrical stages. By using specialized software, a two- or three-dimensional object is spatially mapped on the virtual program which mimics the real environment it is to be projected on. The software can interact with a projector to fit any desired image onto the surface of that object. This technique is used by artists and advertisers alike who can add extra dimensions, optical illusions, and notions of movement onto previously static objects. The video is commonly combined with, or triggered by, audio to create an audio-visual narrative.