I am a new GM, new to RPGs. I am prepping for the beginner game plus Lure of the Lost. I was looking at the table that shows each character's Emotional strengths and weaknesses. How is this best used? It seems like it would be good background for each character. Do I give it to them? Do I use it subtly in their Role Playing to give or remove conflict?

The Emotional strengths and weaknesses are part of the Morality system, and geared towards how a character deals with potential Conflict situations.

But how is the GM to use this practically. Is it meant to be shared with the PCs or just referred to? What if the players interpret their characters differently? Is this a guide on how to role play or a guide for the GM to give or remove conflict?

Both.

You can be as strict or loose with it as you and your players want. You can ignore it entirely. What's useful about it is it might help the player "live" their character in an interesting way, but others find such restrictions burdensome. The beauty of RPGs is you can pretty much toss out everything except the conflict resolution mechanic (e.g.: rolling dice and adjudicating the results), and still have fun with it.

So don't worry if you don't understand that yet, save it for another session if you find it confusing.