Missionaries are people who travel to other areas to try to spread their religion.
Typically, missionaries are more associated with the Abrahamic religions. These religions, perhaps more so Christianity and Islam, are quite sure that their given religion is the only correct way of associating with the divine. Adherents typically feel that those not following the teachings of their religion are in the wrong and will be doomed to Hell for their lack of belief. This belief, within the confines of the given religion, is justified. The sacred texts and often the leaders of these religions proclaim that followers of false gods (any other god but the Abrahamic) are doomed. It is for this reason that devout followers of these religions often take up the role of missionary in order to spread their religion to those who they feel need to hear it to avoid hell. This is in contrast to most pagan and neo-pagan religions. Historically, these religions have been far less oriented towards spreading their faith. Adherents were more of the mindset that "We'll keep to our gods, you keep to yours!" While they didn't follow foreign gods, they might not necessarily claim that they didn't exist or that they were the wrong way to peace and happiness in the afterlife. Because they didn't feel that others were wrong, they didn't really feel the need to spread their religion.
Missionaries often accompany conquering armies, as in the case of those who came with the Spanish to the Americas.