Trade interest ultimately boils down to people who have assets to buy and sell. This is represented below, with buy orders in green and sell orders in red. Without some way of handling the order flow, there are many questions to be answered, for example:
These questions are traditionally answered with a centralized exchange, where orders can be routed and collected into a bid / ask order book, with the sell orders at a generally higher price and the buy orders at a generally lower price, separated in many cases by a price gap known as the “spread”.
Buyers and sellers know they are getting the best price in markets with good liquidity because they can see the price the last trade executed at, and with the right execution their order should be filled at a similar price or rate.
The price on a centralized exchange is only valid at the geographic location and instant that a trade is made. Market makers compete to locate physically close to the exchange in order to get closer to the "price singularity". This leads to problems such as front running where market makers can see outside open interest enter the market and rapidly adjust prices to make a profit filling the trade. This is due to the fact that information takes time to propagate out from the exchange to market participants, and the closer you are, the better off you are in knowing the current state and depth of the order book.