ADR is the term used in the context of stock markets, full form of ADR is American Depository Receipt. It refers to the receipts which are issued by the bank which is located in America to the people who are interested in buying shares of the company which is not located in USA. These receipts are issued in lieu of stocks deposited by the company desirous of getting ADRs and they are equivalent to the stocks and therefore they are entitled for dividends in the same way as domestic shareholders of the company.
These receipts track the price of the shares in its domestic markets and therefore it is equivalent to stocks and hence any investor who is living in USA and he or she is interested in buying the shares of a non US company can go for this option. For example suppose an investor in USA like the Indian company Infosys and thinks that in future its share price will increase but since he or she does not want to take currency risk than he or she will buy the ADR of Infosys rather than directly investing in stocks of the company.