A quick check of a few minutes on a system's most important functions after each release, to confirm it works at all before any deeper testing.
The name comes from hardware testing: switch the device on, and if no smoke comes out, carry on with the other checks. In software it is a very small set of checks answering one question: is the system standing? Does the home page open? Does sign-in work? Can an item be added to the cart? It does not go into detail or rare cases.
Its value is speed: five minutes after each release catches the big disasters before customers see them, and gives you an immediate decision to carry on or roll back. It suits scheduling well, for example every morning before the working day starts. You will find a practical list in the website testing checklist, and the QA Engineer can run such checks on a schedule. Practical tip: keep a smoke test to ten checks at most. If it grows longer it becomes a regression suite and loses its only advantage, which is that it gets run every single time without hesitation.