Dust refers to very small fractions of cryptocurrencies that have a very low value. Due to this low value, in contrast to the transaction costs, it is not worth transferring these small cryptocurrency denominations, which is why they often remain on the wallets of numerous investors.
However, Dust transactions can also be carried out in the context of so-called dust attacks, whereby numerous small fractions of cryptocurrencies are transferred to private wallets in order to subsequently track movements in these wallets and gain information about the wallet holders identity.
See: Proof of Work (PoW), 51% attack.