The Bahnhofsmission (train station mission, mission in the religious sense) is over 100 years old and began as a Christian network to help out young girls moving into the cities who were searching for work and were prone to be exploited for low/unpaid work or prostitution. Train stations were hot points for social problems because they connected and still connect people coming from everywhere.
The Bahnhofsmission tries to help everyone (!) with everything (!) without looking at their backgrounds and uses both staff and volunteer workers. It starts by you asking them for a pencil, for a map, or for a warm place and it ends with support if your train is out of order, the train had an accident, or you are the victim of a crime. As a Christian organisation, it is supported by both by Roman Catholic and the German Protestant churches. For this reason, you can expect a religious environment: bible and crosses. As clarified in the comments, this does not mean that they try to evangelise,
they simply want to convince by action, not by words. They will gladly talk about their background and the Christian idea if you are curious and interested, but if you don't want to be bothered with that, they won't bother you.
Given the extremely broad mission (essentially they are do-it-all) and the different people involved, it is often quite perplexing because you can find beggars, stranded people, and normal tourists. It is also said without a word that more important problems are tackled first, so, if you only need information, it could take some time.