A market is made by use of order books. On exchange there are people who bid and ask. Bid means they place a bid to buy at x price. Ask is a sell at Y price. Since there's a disparity between the bids and ask, those orders sit on the books until someone takes the other side.

The intersection of the bids/asks is the spot price. A market is "made" when a market maker places bids/asks onto the order books. They literally create a market for purchases or sales by placing orders on the order book. Usually a market maker is employed by the exchange to keep volatility in check. The market maker will also take the opposite side of a "market buy/sell" (purchase/sell at spot price).