A merger is the process of uniting two or more pages into a single page. It is done by copying some or all content from the source page(s) into the destination page and then replacing the source page with a redirect to the destination page.
Any editor can perform a merger. No permission or discussion is needed if you think the merge is uncontroversial; just do it (but it might get reverted). Otherwise, the merge should be first proposed and discussed, as detailed below.
When performing a merger, one should remember to reconcile talk pages, and to attribute copied content, as required by Wikipedia's license. At minimum, this means adding words "Merged content to/from [[page]]" to edit summaries. See How to merge below for details.