The scalability trilemma is a phrase coined by Vitalik Buterin (founder of Ethereum) to describe that it is not possible to equally maximize the three desirable attributes that are decentralization, scalability, and security. The trilemma claims that blockchain systems can maximize two at the expense of the third attribute. Therefore, all blockchain systems require trade-offs depending on the specific application and use case of the blockchain system.

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Desirable blockchain attributes

Decentralization: This allows for control and storage of the data to be distributed across multiple nodes in the network. With this property, the blockchain is censorship-resistant, and democractic as anyone can participate in the decentralized ecosystem without prejudice. This is the core and nature of blockchain technology.
Scalability: For blockchain to be used for mainstream applications such as being a payment system, it needs to be able to process thousands of transactions per second. When a blockchain system is highly decentralized, scalability becomes a challenge as the ledgers on all nodes have to be updated concurrently. The less nodes you have, the more scalable the system as it is quicker to update 10 rather than 1,000 distributed ledgers.
Security: For the data on the blockchain to be trusted, the data should be protected from being leaked, lost or modified. It should be immutable and resistant to hacks (i.e., 51% attacks, Sybil attacks, DDoS attacks, etc.). This is a basic and essential requirement.

Trilemma trade-offs

Decentralized & Secure. A decentralized, secure and non-scalable system describes the Bitcoin and Ethereum network. It is difficult to use Bitcoin and Ethereum as a commercial payment system as each transaction can take 1 hour or 5 minutes, respectively. In comparison, the Visa payment that can process 65,000 transaction messages per second.

Security & Scalability. A secure, scalable, and centralized system describes existing commercial database offerings such as SQL, Oracle, SAP. The closest blockchain equivalent would be Hyperledger. The data stored in these systems are managed by database administrators and may be stored in a couple of locations as backups, but not hundreds or thousands of nodes in a decentralized system.

Scalability & De-centralization. New blockchains such as NEO, EOS, or Tomochain sacrifice some decentralization for scalability. For these blockchains, the consensus mechanism is a Proof-of-Stake or Delegated-Proof-of-Stake process with master nodes. The number of master nodes on each blockchain system defines how decentralized each blockchain system is. The number of master nodes for Neo, EOS and Tomochain are 7, 15, and 150.

Conclusion

All blockchain enthusiasts recognize the importance of improving scalability for blockchain to be applied in the mainstream; however, the best method to resolve the scalability challenge and what the trade-offs should be are still up for debate.

Desirable blockchain attributes

Trilemma trade-offs

Conclusion

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