Performance Mapping: Changing engine parameters in order to improve engine performance. These changes are made to maps in the Motronic systems operating code. Hence the phrase "mapping" or more accurately "remapping". 

What are maps?  Maps are lookup tables designed to make an ECU run faster. In computer science, a lookup table is a data structure,  used to replace a runtime computation with a simple lookup operation. Instead of the computer making dozens of calculations, the computer goes to a map (lookup table) and downloads the answer. The  gains are significant. Retrieving data from memory is faster than making multiple computations. 

Lookup Tables: A classic example is a trigonometry table. Calculating the sine of a value every time a sine is needed can be prohibitively slow. Lookup tables are also used by math co-processors, and an error in a lookup table was responsible for Intel's infamous floating point bug (the Pentium Bug).

Porsche uses the term DME. BOSCH & BMW uses the term ECU.  They are tow names for the same thing.  I tend to drift aimlessly between DME and ECU.