What is the $10,000 minimum? Do I need to invest that much?

The $10,000 minimum applies to the company raising funds, and not to the investors.

The ​$10,000 ​minimum is in reference to how much a company needs to raise in order to successfully close their Netcaptial funding round. If a company raises $10,000 or more, investors will receive their shares after the company reaches its close date. If a company does not reach the $10,000 minimum, then investors will get their money back. 

The $10,000 minimum does not mean investors must invest $10,000 in the company. The minimum investment amount for investors can be found on a company's offering page below the yellow "Invest" button (ie. $99 minimum investment).