Once the data is collected and obtained to this step via your pre-set connectivity, then it is all logic to process this data. Based on the data that you are collecting, the processing of this will be dependent. For example, if your incoming data is temperature then the probable example for data processing is to check whether it is within a permissible limit or not.
Local processing devices are the second and third level in IoT. At this point, data is locally stored and processed, ideally not sent forwards unless relevant. This part is explained in detail in the hardware section, as said devices are nothing more than microcontrollers and embedded boards, which handle the data they receive from the sensors.