Whenever someone posts a message, photo, or event to a group you are a member of, Realm will notify you. You control how you are notified, however. If you have set your preferences so that you receive email notifications, you will get an email at your personal email account. This is only a notification, not a regular email to which you can reply.
Near the bottom of the notification, you will see a message “View and comment on this post on Realm Connect.” That is a clickable link which will launch Realm and allow you to post your reply to the group. You can also go into Realm and see the post in the Group’s newsfeed where you can respond to it.
Think of it as you would a notification about a Facebook post–to see the post and reply to it, you must go into Facebook.