So you're wondering why you would want to check the Save a copy of my forwarded email checkbox from the settings screen of your webmail account?
This is best described with an example...
Let's assume that you are hosting your website, VeryProfessionalWebsite.com, with us and you have an email address there called sales@VeryProfessionalWebsite.com.
Let's also assume that you have used a Yahoo email account for years. You prefer the look and feel and would like to consolidate your email in one location especially since you have it open on your computer most of the day.
But your email address is not very professional - You_Suck_73@yahoo.com.
So a prospective buyer comes to your website, emails you at sales@VeryProfessionalWebsite.com and you receive the forwarded email in your Yahoo inbox. Eager at seeing your first sale you hit reply from Yahoo and let the prospect know how professional you are.
The problem? That client just received an email from You_Suck_73@yahoo.com instead of sales@VeryProfessionalWebsite.com.
There are ways around this problem that we can discuss with you but in general we recommend keeping your personal email (Gmail, Yahoo, AOL, etc) separate from your business email so things like this don't happen.
So to answer your original question, you would want to save a copy of your forwarded email so that you can get an alert about the new prospect in your Yahoo account and then log in to your business account to send an appropriate reply.