Preference or preferred shares are shares in a company that have a fixed rather than a variable dividend.
Updated August 2018
Ordinary shares give an investor part-ownership of a company, the right to vote on various decisions (usually though see above for disturbing exceptions), and a share of the dividends. However, firms may also issue other types of shares, including preference shares (sometimes shortened to "prefs").
In the UK and US, these are usually non-voting shares that pay a fixed dividend out of post-tax profits. They have priority when it comes to payments: if a firm does not pay a dividend on its preference shares, it cannot pay an ordinary dividend. The dividend will often be cumulative, which means that if payments are missed, any arrears must be made up before ordinary dividends are paid. If the firm is wound up, preference shareholders get paid before ordinary ones (although the reality is there probably won't be anything left for either once creditors have been repaid).
Less common types of share include participating preference shares, which may get a share of any growth in company profits; convertible preference shares, which can be converted into ordinary shares under certain conditions; and redeemable preference shares, which the company can choose to buy back on certain terms.
Since most preference shares pay a fixed dividend, they behave very similarly to bonds when interest rates and inflation are falling, the price of the preference share will tend to rise, reflecting the increasing value of the fixed payout. However, preference shares are more risky than bonds (as they are further down the pecking order in the event of bankruptcy) and so tend to offer higher yields to reflect this.