"Smoke test" is a term that comes from electrical engineering. It refers to a very basic, very simple test, where you just plug the device in and see if smoke comes out.
It doesn't tell you anything about whether or not the device actually works. The only thing it tells you is that it is not completely broken.
It is usually used as a time-saving step before the more thorough regression/integration/acceptance tests, since there is no point in running the full testsuite, if the thing catches fire anyway.
In programming, the term is used in the same sense: it is a very shallow, simple test that checks for some simple properties like: does the program even start? Can it print its help message? If those simple things don't work, there is no point in even attempting to run the full testsuite, which can sometimes take minutes or even hours.