For example in a 2-for-1 stock split, each existing share becomes two shares. Although the shares outstanding now increases by the multiple, the market capitalization of the company remains the same as the share prices are divided by the multiplier (halved, for example, in the case of the 2-for-1 split).
The justification for a stock split is that the increase in the number of shares leads to greater liquidity, and therefore a greater volume of trades. This can lead to a higher stock price in the short term. The lower price per share also makes the company more accessible to some smaller investors.
There can be reverse stock splits. A 1-for-3 split, for example, replaces every three shares with one. Since market capitalization remains fixed, the result is a higher stock price. This sort of action is done mostly by companies with low priced shares to make them suitable for institutional investors.