You need to understand their are two types of email - plain text and html.
A plain text email is just that, the text can only be wrttten as plain text, no fancy colors, fonts, or features. So with this type of email you CANT do as you want.
But there are also "HTML" emails. A HTML email can work just like a web site, so there is the words you see on the screen, and the html "code" under the covers.
So what you are getting is HTML emails and so what you "see" in the email is the word "click" but under the covers the actual web site address is hidden.
So if you are using say Outlook you need to make sure your email defaults for sending and receiving mail are both set to HTML.