I shall try to answer this question in a brief way.
First of all, the mechanic you select *MUST* be a VW specialist. If you think an ordinary mechanic working on Jap cars would rebuild your VWs engine well, you are sadly mistaken. "normal" mechanics trying their hand at a VW engine are bound to screw up in more than one way. I have seen tons of examples.
By complete overhaul, its meant that the whole engine is dismantled. Meaning the crankcase is opened and any worn parts inside are repaired or replaced.
Many people go for a 'half overhaul'. It means the engine is dismantled only half way. That is, the cylinder heads, cylinders and pistons are taken off only. Thus the mech can only fix the valves (in the cylinder head), replace the pistons and/or rings, and replace/try to repair the cylinders.
In a half overhaul, the vital components inside the crankcase, the crankshaft and camshaft are not attended to. Thus any wear in those areas remains. Since the engine works as a whole unit, a crank which does not run as it should (call it out of balance if you may to keep things simple) would result in swift wear of the piston rings. This is why you are being advised to go for a full overhaul.
Having said that, some engines which have led good lives, with few miles on them, may get away with a half overhaul.
It is difficult to explain clearly in words, pictures would have given you a better idea.