Why does my phone say I have to approve this phone from another device?

If this is part of the two-factor verification code sign-in process to authenticate a new product

and or its user's Apple ID, there would not necessarily be an iCloud Keychain or a need for that

password. Because you need not set up an iCloud keychain to verify a two-factor authentication.

The 'trusted device' is an essential element if you go with the newer two-factor security.

And the is where 'the code' enters. Unless you haven't product to be used in this manner.

• Get a verification code and sign in with two-factor authentication - Apple Support

You could choose to not use the later six digit authentication of newer two-factor security

if you have older devices that cannot be used with this process; or cannot verify one that

would be capable of verifying the newer product ~ as this appears to require if done.

This article covers older Two-Step Verification (not authentication) where you have security

questions and need to answer them in order to gain access to your devices or AppleID.

• Two-step verification for Apple ID - Apple Support

And you could set up iCloud Keychain, from within a iOS device or macOS system settings.

But that is not essential to enable either of these, where either one may ask you to approve

in one form or another. {Also: sharing, hand-off, and other inter-device uses under your Apple

ID may require you to approve or use a code. ~ This is not the same as two-step processes.}

PS: Other situations devices sharing files, applications, and internet may also ask for 'an approval.'

Use Continuity to connect your Mac, iPhone, iPad, iPod touch, and Apple Watch - Apple Support

It usually refers to iCloud Keychain -- "approve this iphone".