The reference count is important because today's computers have a finite (and often severely limited) memory size; it counts how many different places there are that have a reference to an object. Such a place could be another object, or a global (or static) C variable, or a local variable in some C function. When an object's reference count becomes zero, the object is deallocated. If it contains references to other objects, their reference count is decremented. Those other objects may be deallocated in turn, if this decrement makes their reference count become zero, and so on. (There's an obvious problem with objects that reference each other here; for now, the solution is ``don't do that.'')
Reference counts are always manipulated explicitly. The normal way is
to use the macro Py_INCREF() to
increment an object's reference count by one, and
Py_DECREF() to decrement it by
one. The Py_DECREF() macro is considerably more complex
than the incref one, since it must check whether the reference count
becomes zero and then cause the object's deallocator to be called.
The deallocator is a function pointer contained in the object's type
structure. The type-specific deallocator takes care of decrementing
the reference counts for other objects contained in the object if this
is a compound object type, such as a list, as well as performing any
additional finalization that's needed. There's no chance that the
reference count can overflow; at least as many bits are used to hold
the reference count as there are distinct memory locations in virtual
sizeof(long) >= sizeof(char*)). Thus, the
reference count increment is a simple operation.
It is not necessary to increment an object's reference count for every local variable that contains a pointer to an object. In theory, the object's reference count goes up by one when the variable is made to point to it and it goes down by one when the variable goes out of scope. However, these two cancel each other out, so at the end the reference count hasn't changed. The only real reason to use the reference count is to prevent the object from being deallocated as long as our variable is pointing to it. If we know that there is at least one other reference to the object that lives at least as long as our variable, there is no need to increment the reference count temporarily. An important situation where this arises is in objects that are passed as arguments to C functions in an extension module that are called from Python; the call mechanism guarantees to hold a reference to every argument for the duration of the call.
However, a common pitfall is to extract an object from a list and hold on to it for a while without incrementing its reference count. Some other operation might conceivably remove the object from the list, decrementing its reference count and possible deallocating it. The real danger is that innocent-looking operations may invoke arbitrary Python code which could do this; there is a code path which allows control to flow back to the user from a Py_DECREF(), so almost any operation is potentially dangerous.
A safe approach is to always use the generic operations (functions whose name begins with "PyObject_", "PyNumber_", "PySequence_" or "PyMapping_"). These operations always increment the reference count of the object they return. This leaves the caller with the responsibility to call Py_DECREF() when they are done with the result; this soon becomes second nature.