What is meant by scalability in blockchain?

Scalability in blockchain means how many transactions per unit of time the blockchain can process. The scalability of a blockchain is an important prerequisite for its mass adoption. But scalability, security and decentralization present a dilemma where it is hard to get all three. The security of a blockchain simply means protection against false transactions. Decentralization means that no single entity is able to control the blockchain.  

Good scalability + good security = poor decentralization

A good example of a payment system like this is credit cards. The transfers are on a centralized ledger 100% controlled by the credit card company. They have excellent scalability. Visa, or example, can process about 1,700 transactions per second. They also have pretty good security against false transactions and if fraudulent transactions happen, they are able to easily roll them back. But what's totally lacking is decentralization. Credit card companies have total control over the ledger and they can easily censor any transactions they choose or are required to by the government.

Good decentralization + good security = poor scalability

Bitcoin is the poster boy of this variant. Bitcoin is very secure against false transactions. The combined hashing power of the network is enormous and changing the ledger to insert a false transaction would require taking over 51% of the network which would be prohibitively expensive. Bitcoin is also pretty decentralized (at least in theory) and this censorship resistant. But Bitcoin's scalability is very poor. The blockchain can only process about seven transactions per second at a high energy and financial cost. 

Good scalability + good decentralization = poor security

A blockchain like this has a high maximum throughput of transactions and no single central entity is capable of censoring transactions. However, because not much is done verify transactions, it is relatively easy to inject false transactions into the chain.