How to use a WD on mac?

I feel like I am missing a very simple piece of information. I bought a WD for mac external hard drive. I understand what a external hard drive is for and what it does. I just don't get how a monitor what it has on it. I basically plugged it in and it started copying my whole computer. This is fine, but I would really like more control. How can I use it more like a USB and just put all of the files I want on it... mostly photos? I feel like it is doing everything without my permission. If I plug it into another computer will I just be able to access my entire computer? Applications and all?