Parachains are application-specific data structures that run in parallel to each other within Polkadot.

Parachains refer to application-based, individual blockchains (although there is no specific need for them to take the form of blockchains) that run in parallel with each other within the whole Polkadot network. Parachains are connected to Polkadot in a “hub and spoke” style architecture, allowing developers to create new and independently functioning networks powered with the same framework as the main chain.
The technology behind parachains is supported by Substrate, a new-generation framework for building blockchains with web3 functionality, which is also utilized to build and develop Polkadot and Kusama
Each parachain is connected with the main chain through the central Relay Chain, which allows them to function independently without compromising their connection with the entire network. You can treat a parachain just like a regular blockchain since it can have its own functionality, token, governance system and other attributes. However, each parachain can still enjoy the security provided by the Polkadot network and be backed by its validator model since it is linked by said Relay Chain. In other words, one is not required to build his own validator community in order to maintain a parachain.

There are also “collator” nodes that assist validators in securing parachains. As opposed to validators, collator nodes do not secure the network. Collator nodes keep a record of every parachain data, select new block candidates and confirm the inputs and status of a parachain along with validators. Moreover, cross-chain message passing (XCMP) enables parachains to interact with the main chains. 

Since the economics of a parachain can be different from the entire Polkadot ecosystem, they can set different transaction fees according to the choice of their own community.

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