What is a smoke testing and what will it do for me?

Smoke testing is a set of basic cheap to run tests that precede actual testing. It aims to verify that the build is deployed successfully and that all test env. aspects are running and ready for the actual test process. It saves you bringing the full extent of your testing wrath down a faulty build and just realizing that you have been testing on a bad env. or erroneously deployed build possibly too late.

Turn it on, see if any smoke comes out.

The term originates in hardware repair and has been applied to software. It's intended to be a quick test to see if the application "catches on fire" when run for the first time. As stated above it's just to make sure you don't waste a bunch of folks time by setting them loose on something that's obviously broken.

Smoke testing isn't performance testing or regression prevention testing.

Smoke testing is a set of your highest priority fully automated tests. Even if your regular build succeeds, it's possible for your product to be broken in very fundamental ways that make it 100% unusable. Smoke tests are designed to test that level of core functionality. A build that doesn't pass smoke tests is very likely to fail a majority of all of your automated tests.

If a smoke test fails that generally means that you're losing productivity because the build is not usable, can't be tested, etc. Smoke test failures tend to require immediate fixes, on the order of hours not days.

The important aspect about smoke tests is that they can be run quickly. You should ALWAYS be running smoke tests of some sort. Many groups have sufficient resources to run a larger suite of tests on their daily or continuous integration builds (which is goodness), but smoke tests should be considered the bare minimum.