Settlement is the process that completes a contract to buy and sell real estate. Legal title transfers from the seller to the buyer, the rates are adjusted and the purchase price is paid.
The seller and the buyer each appoint their own settlement representative. One representative can act for both sides if there is no conflict and both parties consent in writing, but it is usually better for each party to be separately represented.
See What is a settlement? and Settlement agent, conveyancer or lawyer.