com.apple.WebKit.Networking.xpc wants to sign using key "privateKey" in your keychain
*.pfx file is in PKCS#12 format and includes both a certificate and a private key.

When you imported the file to your keychain both the certificate and private key got imported to your keychain.

In general you first select a certificate to be used in an application or website. So in order to sign you in access to the associated private key needs to be granted.
That is why you get a prompt with options: "Always Allow" / "Deny" / "Allow"

For more info see Mac Help topic: Allow apps to access your keychain

Note: my understanding is also limited. 
I came across your AskDifferent question by searching for a solution to an issue that blocks Allowing / Allways allowing access.