I'll give a common example even though the other answers have defined the term correctly.
Preferred shares are most often issued by utility companies.
So, imagine that there is a corporation called XYX Utilities that provides natural gas and electricity to property owners in Kansas.
It might have 1,000,000 preferred shares and 500,000 common shares and a market valuation for the XYZ utilities as a whole of $250 million.
The preferred shares might have a "par value" of $100 per share and a preference of $10 per share. Typically the preferred shares can only vote in shareholder elections if the preference is not paid up to date, and typically, once their preference is paid they also get their fair share of dividends also payable to common stock shares.
This means that upon liquidation of XYZ Utilities, for example, if it was sold for cash to Xcel Energy for $250 million and the cash proceeds were distributed to shareholders, that the first $100 million left over after paying off all of its debts would be paid to preferred shareholders (in equal $100 amounts per share), and the remaining cash would be distributed at $100 per share of preferred stock and $100 per share of common stock.
So, the preferred stock shares would get a total of $150 each, and the common stock shares would get a total of $100 each.
Suppose that XYZ Utilities has a $25 million profit that it decides to pay out dividends. The first $10 million goes to the 1 million preferred stock holders as a preferred dividend. Then, the next $15 million goes $1 per share to each preferred share and to each common stock share.
But, suppose that XYZ Utilities had a bad year and only had $5 million it could spare to pay in dividends. The preferred stockholders would get $5 per share and would be entitled to an extra $5 per share out of the next dividend paid in addition to their regular preference. The common shareholders would get nothing. No one could sue XYZ Utilities for not paying enough.
Preferred stock is basically a substitute for subordinated debt (which are legally enforceable debts that have last priority in a bankruptcy or liquidation before shareholders including preferred shareholders get anything). Holders of preferred stock surrender the ability to sue if its preference is not paid for an ability to vote on dividends and board members in that case. This reduces the risk of XYZ Utilities going bankrupt in a bad year that leaves it with little cash flow. It also provides tax benefits to certain corporations that are institutional investors in utility stocks that aren't available to bond holders.
Most of the time, however, preferred stock is paid as expected which makes it attractive to people looking for fixed income investments.
Also, sometimes the preferred stock has no economic rights other than its fixed dollar per share preference (which has to be paid later if there is a shortfall) and its fixed dollar right value to be paid upon liquidation or redemption of shares (a redemption is a stock buy back by the company), which makes it even more like a subordinated bond preference, but without compound interest or an ability to sue for payment.