It's important if the spaceship is going to another planet or anything else that could possibly sustain life of any kind (e.g., Jupiter's moon Europa). This is because we want to make sure we're not dumping some of our own life forms on that celestial body.

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The same for trips to Mars. If we have an experiment that tries to detect life on anybody we do not what contamination from the earth can give a false positive.

So that no forms of life are brought to the new location which may complicate the search for life on the new planet.

Then along came Elon...

If we find life wherever we go, we want to be certain that it wasn't because we brought it with us.

And if you are talking about the ISS or other potential future long-term manned missions, it is important to make sure you don't carry up any microbes that could potentially screw up a biosystem that is already going to be really hard to maintain.