What does Shluchei mitzvah einam nizokin mean? That one on a way to do a mitzvah will actually never be harmed?!

The Talmud here (Pesachim 8b) literally means that those who are on their way to do a mitzvah will not be harmed, but immediately adds that this doesn't apply to commonplace accidents or mishaps which may happen even in these cases, as we sometimes unfortunately see. Others add that it means that the mitzva itself will not bring him harm, but that doesn't protect him from other damages. In short, don't rely on this saying to miraculously protect you, and you must take the normal precautions, as usual.