Bonus shares are shares issued free of cost to the shareholders of a company. As this is essentially a book entry (reserves get capitalised), following a bonus issue, though the number of shares increase, the proportional ownership of shareholders does not change.
Also, post the bonus, the share price should fall in proportion to the bonus issue, thereby making no difference to the personal wealth of the share holder. However, more often than not, a bonus is perceived to be a strong signal given out by the company and the consequent demand push for the shares causes the price to move up.
As far as tax is concerned, since no money is paid to acquire bonus shares, these have to be valued at nil cost while calculating capital gains.
The originally acquired shares will continue to be valued at the price paid at the time of acquisition. An incidental tax planning benefit is that since the market price of the original shares falls on account of the bonus, there may arise an opportunity to book a notional loss on the original shares. This is known as bonus stripping. It may be noted here that through Section 94(8), the Income-Tax Act has introduced measures to curb bonus stripping, but strangely, the same are only applicable to mutual fund units and not to shares.