What are the advantages of OpenID Connect?

Usability (central login at the OpenID Provider, no extra account), relief for service providers (authentication and user management delegated to the OP), security (TLS everywhere, sensitive data over a protected back channel), native single sign-on for apps, and popularity (mature, widely deployed social logins).

• Usability: users log in centrally at the OpenID Provider with an account they already have, instead of creating yet another username and password. That saves time and effort.
• Relief for RPs: applications delegate authentication and user management (password storage, resets, second factors) to the OP and can concentrate on their actual features. Not storing passwords also means not losing them in a breach.
• Security: all transmitted data and parameters must be protected with TLS, and the sensitive exchange between RP and OP (tokens, user data) runs over a protected back channel.
• Native SSO: an extension (still a draft specification) provides single sign-on across native mobile apps.
• Popularity: mature, widely supported protocols with libraries for every platform; social logins are familiar to users.

The common thread is concentration: authentication happens in one specialised, well-protected place, and every RP benefits from its strength.

Go deeper:

• Social login (Wikipedia) — advantages and disadvantages of logging in with an existing account.
• OpenID Connect Native SSO for Mobile Apps — the extension that shares a login across a vendor's apps.