From Computer History Wiki
An address space is the total namespace available for identifying discrete objects in an information-processing system. (These names are usually termed 'addresses'.)
Most commonly, it refers to the maximum amount of main memory a given CPU architecture can handle directly in a program (i.e. without use of a mechanism such as bank switching); although such CPU's could often/usually handle more memory than one address space's worth.
However, it appears in other contexts as well; e.g. the Internet Protocol Version 4 has an address space of 2^32 names (from its 32-bit addresses).