The rights issue is the process by which a company raises further capital. The thing which makes Rights Issue different is that the rights issue is only available to the existing shareholders of the company. For example, if X holds 100 shares of Y company and the Y company rolls out a rights issue with the ratio of 5:1 (For every 5 shares you can apply for 1 share). In this case, X has 100 shares so he/she can apply for 10 shares.
Now you must be thinking why X would apply for the shares in the rights issue when he/she can easily get the shares from the open market? The reason is discount! Yes, in a rights issue the shares are offered at a discounted price.
Want to know more in detail Read @ How to apply for rights issue?