Citation managers are software tools that help you find, save, and organize the information sources (articles, books, etc.) you need. They do much more than simply generate a citation in a particular style, though they can do that, too! (For accuracy, double-check citations with a style guide.)
A citation manager is great to use when you are working on a large writing project, like a dissertation or other capstone project, for which you need to keep track of many sources.
How do I decide which citation manager to use?
You can find lots of reviews, blog posts, articles, etc. out there about people comparing citation managers. Here's one page that covers the reasons you would choose Zotero, Mendeley, or Endnote. Here is another that compares several different tools.
Cost is certainly a factor in choosing a citation manager. Fortunately, free options like Zotero and Mendeley are robust and easy to use. You may find that a fee-based tool like EndNote is not necessary for you.