What is the purpose of "Schema Owner"? If I create a new schema and set the schema owner to another schema, for example dbo, what is the meaning of that in regards to my new schema?

Does my new schema inherit the same permissions from it's owner dbo?
A Schema's owner is always a User (or Database Role).  There may be a Schema with the same name as a User, because in very old versions of SQL Server a User and a Schema were the same thing.  So there's still a User called dbo and a Schema called dbo in every database.

A Schema's owner is a User who has full control of the schema, and who will be the default owner of every object added to the schema.  Owning an object suppresses permissions-checking on the object, and plays an important role in Ownership Chains.