When the New York Stock Exchange first got started back in 1792 (when men wore wigs and knee socks and texts were called letters and Spotify was a guy who knew how to play more than one song on a harpsichord), people met under a buttonwood tree in lower Manhattan to trade stocks. That's a centralized market: everyone has to get together in one place to get things done.
Nowadays, most of the trading on the NYSE is done electronically. People from all over the world can execute trades without being in the same time zone, or even the same continent. That's a much more decentralized market.
The definition of a "decentralized market" is somewhat vague. Rather than think of it as a hard category, better to think it as a spectrum. Any given market falls somewhere on a scale between centralization and decentralization.
For instance, even though computers and electronic trading have made stock trading much more decentralized than they were in Alexander Hamilton's day, in general, the equity market is far more centralized than many other markets. Trades still clear through a few distinct organizations, and there are regulatory bodies that designate procedures and rules.
Meanwhile, markets like those for cryptocurrencies slide much further toward the decentralized side of the scale (falling somewhere between "Wild West" and "complete chaos"). These markets operate under far less regulation and with far more variance in trading procedures than more structured systems, like those for stocks.
But that doesn't mean that new-fangled stuff trades in decentralized markets, while older stuff always trades in a more centralized one. The market for baseball cards, for example, would be an example of a decentralized market, since a large portion of those transactions take place on a person-to-person basis, with no governing regulatory framework or central clearing authority.
See: NASDAQ; See: ECN.