These are the shares in mainland China-based companies that trade on Chinese stock exchanges like Shanghai Stock Exchange and the Shenzhen Stock Exchange. A-shares are usually only available for purchase by mainland citizens; foreign investment is only permitted by a tightly-regulated structure called as Qualified Foreign Institutional Investor (QFII) system.
Most companies indexed on Chinese exchanges will provide two shares classes: A-shares and B-shares. B-shares are quoted in foreign currencies (like the U.S. dollar) and are open for both domestic and foreign investment (given that locals establish a foreign currency account), whereas A-shares are only quoted in Chinese renminbi.
A-shares experienced volatile growth in the 2005-2007 periods as limitations preventing investment by Chinese citizens slowly started to peel away. In fact, demand was very high for A-shares that they would trade for higher valuations than what the same stock could be bought for on a different exchange.