Most people understand what a business process is but when you combine it with re-engineering, it suddenly sounds vague.
The ProSci-sponsored BPR Online Learning Center calls a business process “a set of activities that transform a set of inputs into a set of outputs (goods or services) for another person or process using people and tools.”  
It is simple. The way we interpret that is:
<li>there are many ways of doing business,</li><li>when one of those ways does not work or is considered to be ineffective it has to be improved,</li><li>certain elements are introduced to make it better (“inputs”),</li><li>those elements translate into a better product or service,</li><li>that product or service is supposed to serve another person (a customer, a supplier, a partner)</li>
That’s elementary enough, but why do business processes have to be re-engineered?
It’s All About the Customer (and Competition)
The philosophy behind business process re-engineering is to please the customer.  By delighting him, we get to keep him, turning him into a loyal disciple.
Rivals have a sneaky way of snatching customers away from us.  It’s not because this world is full of sly and evil people, it’s because we tend to sit on our bottoms and think that we’ve finally got it made.  We’ve become lax.
Business process improvement, according to ProSci, is not be confused with business process re-engineering.  Instead of improving on current processes, the re-engineering concept says that because the technique is no longer viable, it has to be replaced, abandoned.  There’s a need to establish a clean slate, as the BPR Online Learning Center teaches us.
Business process re-engineering, just like the DMAIC in Six Sigma, presupposes a series of stages:  stage 1 involves a definition of the project – its rationale, objectives and scope.  Stage 2 covers the entire learning process wherein we obtain as much information as we can about our employees, customers, suppliers and competitors – including non-competitors and align that new information with technology.  
Armed with this knowledge, the next stage – stage 3 - is to set up our mission.  Others call it a vision of the future.  This requires a new set of business processes.  Once we’ve determined the desired outcome of this transition, we move on to the next stage which calls for a plan of action that allows us to measure the gap between our company’s present state and where we want it to go.
When we get to this stage, solutions logically follow.  
If you’re still wondering what distinguishes business process improvement from business process re-engineering, think of the starting point:  are you starting from an existing process and want to improve on it, or do you want to start from scratch?