It's used to replicate the Kanji before it. For example, われわれ can be written 我々 or 我我, せんせんしゅう→先々週 or 先先週, ひとびと→人々 or 人人..etc.

Dictionary tip: while it's true that 々 duplicates the character in front of it, and you could use two characters instead of the duplication character, many words are almost always written with the duplication character and rarely with two duplicated characters. For example 人々 is rarely written as 人人。This can be a problem when you're looking up words in a dictionary or searching for things online because the 々 character doesn't have a standard keyboard representation. It's worth figuring out how to do it on whatever machine you use though because just duplicating the preceding character often doesn't work. On the Mac platform (and IOS devices) I use "おなじ” which will cause the 々 character to appear as a drop down option.