iPhone: What is a WWDR intermediate certificate?

In the Apple Developer Portal, in Certificates, Developer (or Distribution) it says:

"If you do not have the WWDR intermediate certificate installed, click here to download now."

I don't even know what that means. Do I need to download and run that? or do I need to only download the current certificate only?

You need to download it and double click on it. It will get stored in your computer's KeyChain. It can be described best as something like root level certificate authority that affirms that your development or distribution profile certificate was issued by Apple's WWDR and not forged somewhere else.

iPhone Game Development book says:

WWDR certificate

Apple’s World Wide Developer Relations (WWDR) certificate is available from Apple at http://developer.apple.com/certificationauthority/AppleWWDRCA.cer. Download and install the certificate so that you can use it to certify builds. The WWDR certificate links your development certificate to Apple, completing the trust chain for your application.

The WWDR certificate is needed to tell Xcode that your other certificates are valid. You need to download them all and drop them on your KeyChain.

WWDR certificate is required since it contains the public key of the Certificate Authority(CA).Here the Certificate Authority is Apple itself(Apple Root CA).
This certificate is to ensure that your Development and Distribution certificates are indeed issued by the CA and the owner of that certificate(ie your identity) has been verified.
wiki regarding Certificate Authority

As per Apple :

To help protect customers and developers, we require that all third party apps, passes for Apple Wallet, Safari Extensions, Safari Push Notifications, and App Store purchase receipts are signed by a trusted certificate authority. The Apple Worldwide Developer Relations Certificate Authority issues the certificates you use to sign your software for Apple devices, allowing our systems to confirm that your software is delivered to users as intended and has not been modified.

Source : https://developer.apple.com/support/certificates/expiration/