To explain makers and takers concept I would take help of Mary Maker and Terry Taker. Mary wants to buy ( or sell ) BXL token ( Blockx Labs token ). Mary creates BXL Order doesn’t matter buy or sell. This makes Mary maker for the Exchange. Terry who just came back reading important announcements about Blockx Labs sees and interested in completing the order. Terry accepts the order and becomes Taker for the exchange.
To be identified as maker or taker buying or selling does not matter but if participant is creating or accepting the order. Generally speaking adding or taking liquidity. Liquidity creator is Maker and liquidity reducer is the Taker.
Centralized Exchange
In above example Mary created example absorbed by Central Software. If anyone wants to trade they have to talk to this Central Software. Central Software makes exchange centralized. While blockchain is running on tens of thousands of node a central server runs on way less nodes, possible only 1 server. Central server is generally owned by person or single entity. Such entity can be scrutiny and forced to censorship. Central entity could be target of attack by malicious group of people, country easily. Hence decentralized exchange provides more freedom and universal participation.
Decentralized flow
Everybody is running Central Book. Mary publishes to Terry and all other participants Central Book directly. When Terry accepts the order settlement happens on blockchain directly. All participants completes the trade without any Central Book.
Complications in Decentralized Flow
If Mary wants to sell BLX and Terry agrees. Terry would send Ether to Mary but Mary maliciously refuses to send BLX. The trust is missing and immediate settlement is missing. This is the missing piece of decentralized exchange.
Conclusion
Participant creating liquidity to the exchange is making the market hence he/she is the Maker. Otherwise participant is removing the liquidity hence he/she is the Taker. While centralized exchange provides trust limited by censorship and on hacker’s target, the decentralized exchange has a problem to solve for trustless participants.