mod_mapnik_wms is an Apache module for operating a Mapnik based WMS server. It was initially written by Frederik Ramm for internal Geofabrik use, but now is available under the GPL from Github geofabrik/mod_mapnik_wms. See there for instructions on how to run it.
WMS (Web Map Service) is an OGC standard for serving maps. Essentially, it specifies a set of HTTP URL parameters used by a client to retrieve a map image from a server.
mod_mapnik_wms will accept such a HTTP request, issue the requisite calls to the Mapnik library to render the requested image, and return the image to the HTTP client.
Maps created in this manner are much slower than those created with a tile server, but WMS offers more flexibility in terms of map projections and resolutions.