Impact on the Stockholder
Just as a Stock Split maintains the same market capitalization for the company, it maintains the value of the stockholder's portfolio by doubling the number of shares he/she owns.
If you owned 1,000 shares of XYZ at $100 when it splits, you owned $100,000 worth of stock. When it splits, your shares are doubled and you now own 2,000 shares, but the price is now $50 each, which is still $100,000 worth of stock.
However, your stock is more volatile now! If the stock price increases $1, you have $102,000 worth of stock ($51 x 2,000 shares). If the stock price decreases $1, you have $98,000 worth of stock ($49 x 2,000 shares).