What does exactly the "connection" mean here?

The following extract is from "Writers Options for Student Daiker" by Andrew Kerek, Max Morenberg and Donald A Daiker. I just don't know what exactly the "connection" means.



Version (1): Marie was sitting at her desk. Her head was slightly lowered over a pile of chemistry notes.

You like your opening sentences, but you want the fact that 'Marie was sitting at her desk' more closely connected to the detail of 'her lower head'. At first, you try to make this connection by simply joining the two sentences:

Version (2): Marie was sitting at her desk, and her head was slightly lowered over a pile of chemistry notes.

You're not altogether happy with this version either, so you try again. Eventually you write something like this:

Version (3): Marie was sitting at her desk. Her head slightly lowered over a pile of chemistry notes.

You may like this version best, both because it is concise and because it clearly connects Marie's sitting at her desk' to her lower head.

To me, in terms of meaning, these three versions are connected to the same degree. They are just orthographically different. Can you tell me what exactly the "connection" means?

Thanks for your help.