I read somewhere that we are completely different to when we were born, because over the course of our lives everything in our body turns over. Our skin is shed, our cells are replaced, etc.

I wonder if this is true or not? And if it is true, can you tell me, are there some bits that aren't. I can think of two things I think that can't possibly be (or that's what I think) and this is tooth enamel and white blood cells (for their memory perhaps of diseases).

I did have an argument about this with a friend of mine and I hadn't really thought about that, but it seems like a really interesting point if it is true.

Also, do you know of any scientific journal or good quality press articles on this thing. I am not really sure what area of biology this is from, so I just posted it here.

Last question and I think this is probably not going to be able to be answered, and that is, what difference does it make if it is true. I am guessing that it is irrelevant in some ways since  we are just the same 'person' and maybe that is just a psychology or philosophy thing?

live science tends to be fairly reputable, and they have a short article here:
http://www.livescience.com/33179-does-h … years.html

Simply put, most cells do get replaced, but some, importantly the neurons in the brain, do not.  I think your suggestion of enamal is correct, but white blood cells do die and get replaced (apparently every year or so).

I suppose it may depend on your definition of replacement (e.g., partial, total, functional) but there is neurogenesis in a few brain regions of adults, e.g., in the olfactory lobe (see - http://www.ncbi.nlm.nih.gov/pubmed/25339754; http://www.ncbi.nlm.nih.gov/pubmed/25297106) and in the hippocampus especially after exposure to chronic or repeated stress (e.g., see - http://www.ncbi.nlm.nih.gov/pubmed/25251485).