The Killer Convention was introduced by The Times, shortly after they published their first Killer Sudokus.
There was some confusion regarding repeating digits within a cage. Most cages could only contain one of each digit, because they were located in a single row, column or box. Some cages had shapes that would theoretically allow multiple instances of a single digit.
To put an end to this confusion, the Killer Convention was introduced. It states:
No digit can appear more than once in a single cage, even when it is allowed by the normal Sudoku rules.
Most publishers are following this convention, and most Killer computer programs also enforce it. There are still a few Killer publishers who do not follow the convention, so you may occasionally encounter Killers that cannot be solved when you apply it.
Unless otherwise specified, Killer material on Sudopedia will follow the Killer Convention.