Moving email settings from one Apple Macintosh computer to another requires a bit of legwork. Since Mail (also called Mail.app or Apple Mail) doesn't have a built-in export feature, you'll have to locate two separate files to copy over to the other Mac. Here is how.
Click the "Finder" icon on the dock to launch a new Finder window.
Navigate to your account's Library folder in Mac OS X's Finder. Under Places, click your username (the one with the house icon) and then click "Library." You can also do this by selecting "Go" from the Finder's top menu and then "Go to Folder." Type in "~/Library" (without the quotes), and it will open up the Library folder.
Find the "Mail" folder.
Copy the entire "Mail" folder onto a storage device (USB thumb drive or blank CD-R) or transfer it over the network to the same place (User:Library) on the other Macintosh computer.
Go to the Preferences folder in the Library and locate the "com.apple.mail.plist" file. You can navigate there using the Finder window or select "Go" from the top menu of the Finder, click on "Go to Folder" and type in "~/Library/Preferences/" (without the quotes) in the prompt.
Copy the "com.apple.mail.plist" file onto your USB thumb drive or CD-R or copy it directly to the User:Library:Preferences folder on the other computer over the network. "User" is your user account name.
Plug in the USB thumb drive or insert the CD-R into the optical drive on the other Macintosh computer if you haven't transferred the files over the network.
Move the "com.apple.mail.plist" file to the User:Library:Preferences folder of the other Mac. "User" is your user account name.
Move the Mail folder to the User:Library folder on the other Mac.
Launch Mail.app. Now your settings and email should be the same as those on the old Mac. If not, make sure both the Mail folder and the "com.apple.mail.plist" file are in the correct places.
You can also use these steps to back up your email and settings. Instead of transferring and moving the files, just back them up to a disk or another portable hard drive.