It's a bit late, I know, but I'm sure that heathfield was wrong in saying that the apostrophe (indicating possession) stands for 'his' or 'its'. I believe that it indicated (originally) an omitted 'e' from the German genitive case which generally adds -es to a noun.
I agree with those who say Tesco's is a shortened version of Tesco's store. Just as you would say "I'm going to the butcher's", or "I'm going to the greengrocer's", you say, "I'm going to Tesco's." It's a bit odd that we don't say, "I'm going to Asda's"