Keychain is a password management system for Apple's macOS. Dropbox requires access to your Keychain to help verify your account and to provide another layer of security over your Dropbox application settings.
To grant Keychain access to Dropbox, simply click Allow or Always Allow (recommended for seamless access) when prompted to do so from macOS.
Clicking Deny will result in a "Couldn't start Dropbox" error message. For security reasons, Dropbox will not start without access to your Keychain.
For more information about macOS Keychains, consult Apple's Support Center.