iCloud Two-Factor Authentication
Since 15 June 2017, Apple requires that all third-party apps syncing with iCloud use app-specific passwords. This includes Contacts+.
To create an app-specific password:
1) Go to https://appleid.apple.com/ and sign in.
2) Scroll down to Security, then click Generate Password under App-Specific Passwords.
3) Create an app-specific password for Contacts+.
4) Copy and paste that password into the password field on Contacts+ when you connect your iCloud account.
For more information on two-factor authentication, visit Apple's website.