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!
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. One good one compares Zotero to 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.
Choosing a citation manager is a personal decision that should involve comparison, experimentation, and a real idea of what it is you want the software to do for you. Even most of the fee-based tools offer free trials, so don’t be afraid to test out various tools before you decide which one best fits your needs.