A smoke test is a quick check that the most important parts of an app are working after a change. It is like turning on a new appliance and checking that its basic controls respond before using it for a full job.
For a website, a smoke test might open the home page and check that sign-in and the main navigation appear. It can reveal a major problem early, before someone spends time on deeper testing.
A passing smoke test is only a quick signal. It does not mean every feature or unusual situation has been checked.