When you see stock market bid and ask spreads quoted (say for equities), how is it that the spread is collated?

In other words how does the willingness of many thousands of buyers and sellers to transact at prices individual to themselves translate into a single spread - what is the chain?

For most stocks, there are one or more market makers that offer to buy or sell equity at the prices they fix. The quotes are adjusted regularly, and the spread depends generally on the volume in that particular market.