Subscribe can be overloaded to serve a dual purpose. I'd prefer if these concepts could be distinct, but unfortunately not so with vBulletin.
There are useful widgets on the lefthand nav of
Settings, including a "Subscriptions" one. (It's a little counter-intuitive there, IMO, as these nav functions are distinct from what you generally want to change for 'Settings', but I haven't found a way to make it show elsewhere. I digress...) By default, there is just one big folder 'Subscriptions'. You can add more with the "
Edit Folders" link underneath of it.
Under '
General Settings', you can tune the frequency at which you'll receive email about subscriptions, including all the way down to 'none'.