Smoke testing is a relatively simple check to see whether the product "smokes" when it runs. Smoke testing is also known as ad hoc testing, i.e. testing without a formal test plan.
With many projects, smoke testing is carried out in addition to formal testing. If smoke testing is carried out by a skilled tester, it can often find problems that are not caught during regular testing. Sometimes, if testing occurs very early or very late in the software development cycle, this can be the only kind of testing that can be performed. Smoke tests are, by definition, not exhaustive, but, over time, you can increase your coverage of smoke testing. A common practice at Microsoft, and some other software companies, is the daily build and smoke test process. This means, every file is compiled, linked, and combined into an executable file every single day, and then the software is smoke tested. Smoke testing minimizes integration risk, reduces the risk of low quality, supports easier defect diagnosis, and improves morale. Smoke testing does not have to be exhaustive, but should expose any major problems. Smoke testing should be thorough enough that, if it passes, the tester can assume the product is stable enough to be tested more thoroughly.
Without smoke testing, the daily build is just a time wasting exercise. Smoke testing is the sentry that guards against any errors in development and future problems during integration.
At first, smoke testing might be the testing of something that is easy to test. Then, as the system grows, smoke testing should expand and grow, from a few seconds to 30 minutes or more.