Local versus Global (or world, I use them interchangeably), are basically different coordinate systems. Vertexes can be relative to the objects local coordinate system (this is the default because of how OpenGL works), or to the global one (which is how we get trained to think about coordinates). Without going into too much math, it suffices to say that you can consider local to be relative to the objects center, taking into account its rotation and size, while global is relative to (0,0,0) (the origin).
Here’s a quick demo (make sure you select a mesh object like the default cube):
scn = bpy.data.scenes.active
ob = scn.objects.active
ob.LocZ += 1
ob.setLocation(0, 2.0, 3.0)
me = ob.getData(mesh = True)
# But wait this isn't where this vert is! Actually it is, but its relative
# to the object's center and orientation (rotation/scale). If we want its
# absolute position, lets transform it to global coordinates
obmat = ob.matrix
print me.verts.co * obmat
# Now its where we want it to be. Its now in global space, relative to the global
# Origin (or (0,0,0))
Read the comments, but also try playing around with some stuff. Look in the N-transform panel as you play around with object locations. Try giving the object a parent and see how that effects whats going on.
For the last part, the main thing to note is that you can essentially apply a transform to a coordinate by multiplying by its object’s matrix (you get absolute world coordinates). Most operations can be performed on relative coordinates since most operations are relative (shift along a normal, translate, etc. can all be done without knowing absolute positions). Sometimes, though, its necessary to know these coordinates.
For most purposes, though, its really not all that necessary to worry about world vs. local when your generating meshes. But for some applications, obviously it can be important to know absolute positions, like when you’re dealing with multiple objects where you need to do manipulations between them. In that case, you want to work in global coordinates between the objects.