private equity specifically does mean stock that is not publicly traded. BUT (and I may be wrong here, so apologies if I am!) I think some of the confusion may be that the term "private equity" is more commonly/generally used to describe private equity funds and their investment strategies.
In that case, private equity funds are essentially investment funds with a strategy something like this (and I'm trying to be as bland in description here as possible, as private equity fund strategies very often result in some unpopular results - ie. mass layoffs, selling for parts, etc.): purchase a controlling interest in a company (often times financing the purchase with debt acquired by the company they are purchasing), operate the company with a super focus on some sort of efficiency (usually profitability or revenue), and then re-sell the company 3-5 years later at a 2-5X return (ideally, of course sometime that doesn't happen).
the reason they are called private equity funds is that in order to get a "controlling interest", PE funds almost always either target (1) smaller private (usually industrial) companies that are operated by their owners (my cousin works at a fund that focuses on oil-services companies that are private but have $100m+ in annual revenue) or (2) public companies that they think are undervalued by the market or poorly run that they can "take private" by purchasing all the stock and then running more efficiently (these are the big sexy PE deals, biggest recent example is: Dell - http://www.forbes.com/sites/connieguglielmo/2013/10/30/you-w...)
there's a WHOLE lot of other details that I won't get into on how PE funds work, and about how PE funds are now so massive that they almost act like unregulated banks and have a bunch of strategies other than the one I described above, but that's the traditional fund strategy (at least based on my experience) and I think a good place to start.
Another good way to learn would be to learn more about the biggest PE funds themselves:
KKR: https://en.wikipedia.org/wiki/Kohlberg_Kravis_Roberts
TPG: https://en.wikipedia.org/wiki/TPG_Capital
Silverlake: https://en.wikipedia.org/wiki/Silver_Lake_Partners (work in tech a lot, did the skype deal where they bought from eBay and sold to MS)
Another way to learn more might be learning how a leveraged buy out (LBO) works, as this is one of the more traditional PE fund financing strategies for their deals: http://www.investopedia.com/articles/financial-theory/08/lev...
If you really get into it, the book "Barbarians at the Gate" is considered a classic book written by two WSJ journalists about KKR's takeover of RJR Nabisco, the largest PE deal in history ($25b in 1988), I enjoyed it!