The Gravity Forms plugin allows you to set up email notifications. Multiple notifications can be set up, so you can have an email go to the person who filled out the form, as well as a separate email go to your staff to let them know that a form was filled out.
If you or your users aren't receiving email notifications through Gravity Forms, there are a few things you should investigate.
Check Your Settings
Follow Gravity Forms' recommendations here. Make sure your email address settings don't have any typos or spaces.
Test With Another Server
If emails aren't getting through to your business email, i.e. email@example.com, try setting up notifications to temporarily go to your personal email, i.e. firstname.lastname@example.org.
When a form is completed and a notification is triggered, Gravity Forms "hands off" the notification to the appropriate mail server (i.e. Gmail or yourorganization.org) and it's up to that server to get the email to you.
Investigate Your Server
If email are getting through to one server but not another, it usually means that there's something going on that's keeping the affected server from successfully receiving and delivering the email notifications. You may need to contact your IT department and see if there are some settings that they can change or look into. Here's a list of different things to try with your server settings, via Gravity Forms.
Understanding Email Reliability
Per Gravity Forms:
There are a huge number of potential issues that can lead to your notifications not being sent or received, and as such, if you've gotten to this point, you are most likely experiencing an issue that is less common and will require the support of your server administrator to solve.