A rights issue is an issue of rights to a company's existing shareholders that entitles them to buy additional shares directly from the company in proportion to their existing holdings, often at a discount to the market price. Rights are often transferable, allowing the holder to sell them on the open market. You have 3 options when considering a rights offering:
If you choose to subscribe you will be able to purchase additional shares, often at a discount.
The actual purchase of rights is not a tax event, however, as there is often a discounted price your overall cost basis may be altered. The sale of rights is a tax event and you will need to report this income as capital gains.