WordPress allows you to communicate with the readers of your blog via its excellent commenting system, but it is not an email client and will not allow you to send or receive emails.
The comment system allows you to collect emails from readers who post messages to your blog, and you can use those emails to correspond with them. However, this must be done through a separate email client since WordPress itself will not allow you to do this.
There are many plugins available that will help you to integrate email with WordPress, though. Many people place their email address in the “contact page” section of the website so that they can correspond with the readers via email.
On this site, I use a contact form plugin instead, which helps to keep my email address private from spammers while still allowing me to receive correspondence from my readers. I can then reply to these messages via conventional email if the messages are legit and not spam.
Most webmasters set up email addresses via the control panel of their hosting company. This allows you to use an email address that corresponds with the domain name of your website. For example, your email might be [email protected], or something along those lines.
So, although WordPress is famous for allowing interaction between the author and its readers, you will need to use another application in order to handle email.