Problem
Drupal 8 has the configuration schema system with schema files that describe configuration so translatable pieces can be identified. With #1905152: Integrate config schema with locale, so shipped configuration is translated committed, locale module uses this to pull in translations from localize.drupal.org and save locally, so shipped configuration is translatable. However for edited configuration or when creating new configuration (your own blocks, your own views, your own contact categories, menus, taxonomy vocabularies), there is no UI whatsoever to translate those. Heck, there is no user interface to translate your site name.
Proposal
Add a configuration translation user interface in core. The module woud build forms off of configuration schemas. The current work can be followed at http://drupal.org/project/config_translation.
This would normally not be proposed but given http://buytaert.net/code-freeze-and-thresholds, there is a possibility to get new features accepted theoretically. Also Dries indicated earlier this would not be a fit for Drupal 8, but some of the rules changed since then. See http://drupal.org/node/1648930#comment-6834410 for earlier comments on that.
Remaining tasks
Most prominently writing tests: #1941678: Add automated tests as well as any other outstanding issues at http://drupal.org/project/issues/config_translation?categories=All which are commit blockers.