What does relationship owner means in bidirectional relationship?

Your first example is normal and correct bidirectional one-to-many/many-to-one mapping. Setting Question to Choice-attribute (“owning side”) is enough to have relationship persisted. Entity graph in memory will be messed until other side of the relationship is read from database again. From the
database point-of-view owner is the entity that is persisted to table that have foreign key column (same for bidirectional one-to-one). In specification this is explained following way:

The many side of one-to-many / many-to-one bidirectional relationships
must be the owning side, hence the mappedBy element cannot be
specified on the ManyToOne annotation.
….
Bidirectional
relationships between managed entities will be persisted based on
references held by the owning side of the relationship. It is the
developer’s responsibility to keep the in-memory references held on
the owning side and those held on the inverse side consistent with
each other when they change. In the case of unidirectional one-to-one
and one-to-many relationships, it is the developer’s responsibility to
insure that the semantics of the relationships are adhered to.

In JPA terms your second example does not have owning side, because of absence of mappedBy. Instead you have two unidirectional relationships which are forced to use same column as store. At least with Hibernate 3.5.6 it will behave following way:

• Setting Question to choice-attribute will not persist relationship.
• Adding Choice to question-attribute will not persist relationship.
• To persist value to "QUESTION_ID" both have to be set (yes, also not-insertable question).