What does “emancipation did not simply transfer ownership” mean?

This is an important distinction.

Imagine:

Before emancipation

Slaveholder:

legally owns enslaved person.

The enslaved person:

is the object of that ownership.

Now emancipation occurs.

There are two logically possible transformations:

Possibility A

Ownership is transferred:

slaveholder → formerly enslaved person

That would mean the formerly enslaved person becomes the owner of himself/herself as property.

That obviously isn't what emancipation meant.

Possibility B — what actually happened

The legal category of ownership of persons was abolished.

So:

slaveholder → no longer legally owns person

and:

formerly enslaved person → becomes a legally free person

Thus:

the property relationship itself disappears.