This is a sub-issue of #1910624: [META] Introduce and complete configuration schemas in all of core.
Problem/motivation
#1866610: Introduce Kwalify-inspired schema format for configuration introduced the idea of config schema. The changelog leads to (hopefully extensive) documentation on the format at http://drupal.org/node/1905070. While there are little cleanups planned for the format overall, the current format is a result of months of back and forths, so it should be perfectly fine to apply it more widely to core.
Proposed solution
Create a configuration schema for block and custom block modules. Block configuration entities should be covered as well as custom block type entities.
Schema in place
None.
Schema not yet in place
Custom block module has custom block types (config entity at core/modules/block/custom_block/lib/Drupal/custom_block/Plugin/Core/Entity/CustomBlockType.php), example config .yml at core/modules/block/custom_block/config/custom_block.type.basic.yml
Block module itself has the block config entity (config entity at core/modules/block/lib/Drupal/block/Plugin/Core/Entity/Block.php, config yml at core/profiles/standard/config/block.block.bartik.login.yml and many others there).