In the following I am going to be less than accurate in a number of ways, sacrificing technical accuracy to provide a basic understanding. It is obvious that you have read a number of technical sources and the very technicalness of the material is making it difficult for you to understand what is a fairly basic and simple concept.
In simple terms the most common use of the word map is to describe a relationship between the things in two different sets. This may be a mathematical function or it may be some other kind of representation and mechanism. The most common that comes immediately to mind is the street map.
A street map is a picture of a particular terrain or area in the real world in which the lines and drawings and words written on the map correspond to actual physical streets and buildings. There is a one to one relationship between the representation of the terrain that is pictured in the street map and the actual terrain.
Looking further we can also see that a street map is a representation of the actual terrain. The actual terrain has objects and details and dynamic processes which the street map does not depict. The street map is an abstract representation of the actual terrain and what is depicted in the street map is only what is needed to fulfill its purpose, to provide a navigational aid for the real terrain.
A number of the examples in the question involve creating a representation with supporting mechanisms so that a person can use the representation and the mechanism translates the person's actions into what is needed for the underlying functionality that is hidden by the facade of the representation.
Memory mapped file I/O allows a programmer to think of a file as a large area of memory, to use a memory representation of a real file. The programmer does not think of the file as a file but instead thinks of it as a large area of memory. The memory mapped file I/O functionality takes care to make sure that when the programmer references a particular memory offset that the corresponding data in the file is accessed.
Memory mapped device I/O allows a device programming interface to be simplified by writing to memory addresses or reading from memory addresses. These writing and reading actions are translated by the underlying memory mapped device I/O functionality into the actual device specific actions needed to carry out the requested service or action.
A bit map is a set of bits which provide a one to one correspondence to the values of some other set. For example the
CreateFile() function of the Win32 API has several bit map arguments that are used to indicate different kinds of file attributes. Specific bits in a bit map correspond to a specific file behavior such as "Open as Read Only" or "Always Create New Empty File". Special constants are provided which are combined using binary bit operations to specify the actual arguments. See CreateFile function and the example source code at Opening a File for Reading or Writing.