CREST is the name given to the central securities depository (CSD) and settlement system that covers shares listed in the UK, the Republic of Ireland, the Isle of Man, Jersey and Guernsey as well as UK government bonds (gilts).
Essentially, it does away with the need for paper share certificates by keeping an electronic registry of the existence of shares and manages the transfer of ownership between buyers and sellers when they are traded.
Strictly speaking, CREST is actually the name of the settlement system only. The operator of CREST and the securities depository is a company called CRESTCo. Since 2003, CRESTCo has been owned by Euroclear, which also owns several other securities depositories and settlement systems in Europe, and is now known as Euroclear UK and Ireland.
However, both the depository and the settlement system are commonly referred to as CREST. Except where it’s important to draw a distinction, this website does the same.