Processing rules are basic if-then-else statements to perform minor manipulations of the data. They were added mainly to map context data variables into Analytics variables. However, you can also use them in simple cases instead of a VISTA rule. With processing rules, you can concatenate, copy or set values in Analytics variables. They must not be confused with Marketing Channels processing rules, which are specific for Marketing Channels.
When I was following the Adobe Audience Manager training, I remember that one of the topics I found most difficult to understand was ID syncing. The enablers spent a lot of time using these words and I could see that it was a key part of any DMP. Once I finally understood what it meant, I felt relieved. Today I will explain this concept, in case you are also stuck.