Replace letters by digits from 0 to 9 so that a correct long multiplication is formed. Same letters must be replaced by the same digits, different letters must be replaced by different digits. Multi-digit numbers cannot start with a 0.
(Rules and example from WPC 2019 IB)
Also known as "Verbal Arithmetics," "Cryptarithmetic," etc. The term "Alphametics" sometimes specifically refers to puzzles where the letter combinations form words.
History of the puzzle
A first known example is from 1864. 
The term "Cryptarithm" first appeared in 1931 in The Sphinx journal. The puzzle was written by Simon Vatriquant (Belgium). (Link to actual puzzle appeared in 1931)
The term "Alphametics" was coined by James A. H. Hunter (USA) in 1955.