ISP said their server needs script for hostname | server name

I would be very grateful for any help to understand what my ISP means by this paragraph they offered as a solution.

My problem is at the moment:
WP 4.0 and Woo Commerce with all Woo plugins as well as theme, suddenly stopped sending email s from the themes contact template as well as all new Customer orders to ONLY email sent via #Domain name email addresses. Any other email address hosted via an ISP works fine, but not via my host using @ my domain emails. My Web Host is also hosting emails. emails used to work ok, for new shop orders, I received new order 1 to 7 no problems. However order number 8 did not arrive and no emails have arrived from shop orders or the contact form ever since. It just stopped working from that point on. this was on 27th July. This is so embarrassing because it is happening to my Client, and I developed the website, having no clue how to fix this.

I contacted the web host and they had a look in my word press admin and then gave me this paragraph below as a resolution to resolve the not receiving email from word press to emails at domain name issue.

This is an update regarding the contact form from your WordPress site. We did further check on your scripts and only email address can be set.

**** The reason why [email protected] is not working, it is because our server needs a script that needs host name or server name since your email account is hosted with us. For this case, please be advised to update your script. We kindly suggest you to use SMTP mail or PHP mail which allows you to set our server and email address for the contact form. ******

Please can somebody help me understand what they are talking about, as I am, in reality a graphic designer and Dreamweaver web designer and I am very New to Word press, I understand a little CSS but have absolutely No clue about PHP It’s all very alien to me, I am happy to to do any little graphic design jobs for anybody who can help me resolve this issue but specifically help me understand this issue so I can progressively learn from it. I am happy to off er my skills and time in exchange for yours, if you have the skill to help me.

Elizabeth – Australia