The immediate intention of the conference was to finalize the admittance of Coridan into the United Federation of Planets. Despite several minor quarrels, Ambassador Sarek of Vulcan, who spoke in favor of Coridan's admittance, cast the final vote. (TNG: "Sarek")
The Babel Conference was originally to have been referenced by Montgomery Scott in TNG: "Relics", as evidenced by the first draft script of that episode. However, that reference was replaced by a mention of the Dohlman of Elas.