Depository receipts represent a company listing its securities (shares, bonds etc) in a foreign stock exchange and mobilizing funds from there. From the Indian angle, DRs represent Indian corporate listing a selected portion of the shares of its company in foreign stock exchanges to obtain funds. Advantage of depository receipts is that they are non-debt flows.
For example, Infosys Technologies was the first Indian company to list shares in the NASDAQ stock exchange of the US (later transferred to NYSE). The Infosys ADR (American Depository Receipt) is trading in the NASDAQ Stock Exchange like the SBI share is trading in the NSE.