The sellers concession usually covers the costs that get paid at the closing table because that's when those funds become available. The buyers bank sends a wire transfer (usually these days) and the attorneys will delegate those funds to various sources like the seller to pay for the property, reimbursing property taxes that were prepaid by the seller, perhaps oil that was prepaid and remains in the tank for your future use, your attorney fee, your title insurance, the real estate commission (deducted from what the sellers side), other fees and taxes....
Basically your loan comes to the closing table like one big bag of money and gets disbursed by the attorneys. (Your attorney protects your interests long sure you are paying for only your share.) If by chance any money happens to be left over, they may write you a check. (Because you are the one paying it all back over time, right?)
Hope that helps!
Best of luck :)
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Senior Loan Officer
STERLING NATIONAL BANK
310 Crossways Park Drive
Woodbury, NY 11797