Understanding Google Apps Domain Alias feature...

Can someone please help me understand what the purpose of adding a domain alias to my Google Apps account might be?

I HAVE READ THROUGH THE GOOGLE APPS SUPPORT SECTION FOR DOMAIN ALIAS SETUP, but I found it entirely confusing and still can't grasp what this feature is meant for?

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Here's a quick rundown of some of the details of my situation:

I did not sign up with one of the Google Apps Partner Hosting companies when I first setup my account.
I purchased my domain name from Network Solutions....
My website is currently hosted on Yahoo! Small Business...
I have one other domain name from Network solutions that I have setup for web forwarding to my primary domain
I have another domain name that I purchased from GoDaddy, who is also hosting that domain
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Part of the help documentation about Domain Aliases says,

"Domain name aliases are additional domain names associated with your primary domain and function with your current set of user accounts. Nicknames are not included."

When it says "associated with your primary domain", what does that mean exactly??
When it says that they function with your current set of user accounts, what does that mean??
And yes, I do not even understand what is meant when it says that Nicknames are not included??

Also mentioned in the help documentation, it states that you can send email from a domain alias using a 'custom from address', using the setup instruction below....

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To display another email address in the 'From:' field, follow these instructions in your email account:

1. Click Settings at top of any page in your email account, and then select the Accounts tab.
2. Click Add another email address in the Send mail as: section.
3. Enter your full name in the Name: field, and the email address you'd like to send messages from in the Email address: field.
4. Click Next Step >>, and then click Send Verification to continue the process.
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What's REALLY confusing about this is that I have already followed the instructions above and have setup several of my other email addresses (such as AOL, Yahoo, etc) so that I can send email using my Google Apps Gmail account and have these alternate email addresses used in the 'From' field of the sent messages - all this despite the fact that I HAVE NOT added any Domain Aliases within my Google Apps control panel....

Can someone please explain this to me?

Any suggestions, help, guidance, support, etc... would be greatly appreciated. Thanks!