Non-fungible assets on blockchains are covered in detail under non-fungible tokens (NFT), the tokens most commonly used to represent them. This page explains the broader phrase and how it relates to that entry.
An asset is non-fungible when each unit is distinct, so one cannot simply be exchanged for another of the same kind at equal value. A house, a signed first edition, a painting or a seat with a specific number at a concert are all non-fungible. A dollar bill, a share of the same class or a unit of bitcoin is fungible, because any one unit is as good as another.
The phrase "non-fungible assets" is wider than "NFTs". It describes the thing itself, while an NFT is the digital record that tracks who owns it. On Ethereum such records usually follow the ERC-721 standard, and the ERC-1155 standard lets one contract handle both fungible and non-fungible items. Linking a token to a physical object, such as property or a luxury good, also depends on law and on whoever keeps the object, which is part of the wider field of tokenization.