Well, In Mapreduce there are two important phrases called Mapper and reducer both are too important, but Reducer is mandatory. In some programs reducers are optional. Now come to your question. Shuffling and sorting are two important operations in Mapreduce. First Hadoop framework takes structured/unstructured data and separate the data into Key, Value.
Now Mapper program separate and arrange the data into keys and values to be processed. Generate Key 2 and value 2 values. This values should process and re arrange in proper order to get desired solution. Now this shuffle and sorting done in your local system (Framework take care it) and process in local system after process framework cleanup the data in local system. Ok
Here we use combiner and partition also to optimize this shuffle and sort process. After proper arrangement, those key values passes to Reducer to get desired Client's output. Finally Reducer get desired output.
K1, V1 -> K2, V2 (we will write program Mapper), -> K2, V' (here shuffle and soft the data) -> K3, V3 Generate the output. K4,V4.
Please note all these steps are logical operation only, not change the original data.
Your question: What is the purpose of shuffling and sorting phase in the reducer in Map Reduce Programming?
Short answer: To process the data to get desired output. Shuffling is aggregate the data, reduce is get expected output.