In addition to the previous answer, which was excellent, I would add that the first exchange reveals not just their closeness, but the sway Lady Macbeth holds over her husband. Macbeth will prove to be a reluctant killer at first, so her influence spurs him to action. Only she knows the words to spur him to action. Portia and Brutus were close in Julius Caesar but Macbeth and his wife are true partners.
Good question. I think, first of all, you see that Lady M really is Macbeth's "dearest partner of greatness" as he calls her in the letter she reads out at the start of the scene. Look at teh way she greets him:
Great Glamis! Worthy Cawdor!
Greater than both, by the all-hail hereafter!
She's desperate for him to be big news, desperate for the crown. And you see this again at the end of the scene, when she actually makes a longish speech telling Macbeth exactly what to do. You're left in no doubt about who's got control over who, who wears the trousers in this relationship:
He that's coming
Must be provided for; and you shall put
This night's great business into my dispatch,
Which shall to all our nights and days to come
Give solely sovereign sway and masterdom.
So there's the ambition, and the power dynamic. Yet more than that, you see their closeness. Without saying many words, each knows what the other means. It's a short conversation, but a lot is understood, even if not a lot is said:
My dearest love,
Duncan comes here tonight.
And when goes hence?
Tomorrow, as he purposes.
They actually do finish each other's sentences. Despite everything, they're very, very close.
Hope it helps!