The scaling problem is covered in depth under scaling blockchain, which describes the main approaches and how different networks have tackled them. This page explains the phrase itself, which is common in crypto discussions and in older debates about Bitcoin.
The scaling problem is the challenge of increasing how many transactions a blockchain can process, usually measured in transactions per second, without weakening the features that make it useful. Public blockchains ask every full node to check every transaction, so raising capacity by making blocks bigger or faster also raises the cost of running a node, which can push out smaller participants. This tension is often summarised as the blockchain trilemma of scalability, security and decentralisation.
The phrase is linked to Bitcoin's block size dispute of 2015 to 2017, when the community split over whether to raise the block size limit, a disagreement that led to the creation of Bitcoin Cash. Since then, most effort has gone into solutions that keep the base chain small and move activity elsewhere, such as payment channels, sidechains and rollups, together known as layer 2, along with base-layer changes such as sharding. Other names for the same issue include the scalability problem and the scaling debate.