Process is a manifestation of time.
Physical world has three spatial dimensions and distinct time dimension, along which it evolves. Digital world has an arbitrary multitude of dimensions, which represent various data contexts. But, whatever data types we consider, time still remains standalone and distinct because it describes unique dynamic dimension of change across all variety of data domains. Process is, therefore, an expression of changes, which data undergo with time.
Time is continuous. For this reason, any change of sufficiently complex system consists of an infinite number of steps. For convenience of representation and analysis it is typical to use various forms of aggregation, which unite smaller changes into distinct blocks having evident observable forms. These time aggregates are often referred as steps of a process. The procedure itself yields a process as a product of quantization of time.
Another crucial difference between time and any other dimension of data is its distinct direction. As a rule, any data can be browsed forth and back. However, change with time is a principal one way road where magic back button does not exist. For this reason, most processes in mathematical sense appear as directed graphs evolving along time dimension.
Business processes are not different in above respects from any other process, apart from specific metadata and modeling methodologies commonly used in BPM field. Therefore, all above considerations apply to business processes as well.