Subscription to excatly what? Events occured in EPiServer (like content added, removed), general user subscription to newsfeed, newsletters?

Yes, Functionality is like newsLetter . Send the mail to list of Mail id at the specific time or any new Products added.

You can subscribe to the PagePublished event, check if it is a product, and in that case do your stuff (prepare a mail or whatever).

Or you could create a scheduled job that once in a while checks for new products.