Before we talk about processes, we need to understand exactly what a process is. If you know exactly what it is, and are familiar with the notion of 'Re-entrancy', you may skip to the next section...
You didn't skip? OK. Lets try to write a proper definition:
The ability to have the same function (or part of a code) being in some phase of execution, more than once at the same time.
This re-entrancy might mean that two or more processes try to execute this piece of code at the same time. it might also mean that a single process tries to execute the same function several times simultaneously. How this may be possible? a simple example is a recursive function. The process starts executing it, and somewhere in the middle (before exiting the function), it calls the same function again. This means that the function should only use local variables to save its state information, for example.