The money buys new shares in the company. Think about it in per share terms. In your example:

- Pre-money there are 1,000 shares, valued at $1,000 each

- The company sells 100 new shares for $1,000 each

- Post-money there are 1,100 shares

So after selling 100 shares, the original owner now owns 1,000/1,100 shares = 90.9%. The new valuation is 1,100 shares * $1,000/share = $1,100,000.