Rights Issue is a secondary capital raising strategy by the company. It gives it's stockholders an option say 1:1 (i.e. one rights issued per stock held) for the outstanding common stocks.
Ex. Say an investor has 100 shares of a company at Rs. 10 per share with a total investment of Rs. 1000. The company's brokers informs him about the option as 1:1rights issued at Rs. 8 per share. The investor exercises the option and now get's 100 shares @ Rs. 8 each. Thus his total investment is now 8*100 + 1000 = Rs. 1800 with 100+100 = 200 shares. Average price of share = 1800/200 = Rs. 9.
If all the investors avail the option than the market price of the share would come down to Rs. 9 per share and the market cap of company for a total initial outstanding common shares of 1 million (now 2 million) would be Rs. 18 million from previous market cap of Rs. 10 million.
The EPS of the company halves if the capital raised is not used as the number of shares has doubled. If the capital raised is reinvested properly and the EBIT increases than the EPS also changes accordingly.
As used by the investor, these are an offering of shares issued at a special price by a company to its existing shareholders in proportion to their holding of old shares. 
Investors in common stock occasionally receive rights offerings to purchase additional common stock below the existing market price. The stock rights were probably issued to satisfy the investor’s preemptive right to maintain an existing level of ownership in the company. Rights are issued below the existing market price to encourage the exercise of the rights. The rights are separate having their own markets. 
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