Want subscribers to get emails

OK. I am still fairly new to WP, and have a question, without sounding too green.

I want to have people that I know subscribe to my blog. I have the orange and white logo on the upper right corner, where people can click. I was hoping to see something like, “Get an email every time a post goes up.”

I am pretty web savvy, but am missing something here. Can someone please tell me how this subscription should work? I understand the concept of RSS feeds, where the posts get delivered to other sites and social networking sites, but many of my clients don’t have them.

Can someone please shed some light on this for me?

Thanks