When a company initially establishes itself as a corporation, it has to prepare something called the Articles of Incorporation. These "articles" are filed with the Secretary of State in whatever state they chose to incorporate in (Delaware is a popular state for incorporation).
Articles of Incorporation must include a section called "Capitalization". Capitalization is the process of selling shares to investors to "raise money" in order to run the business. This is a great alternative to having take out loans from banks and having big debt & interest payments each month.
In the Capitalization section of the Articles of Incorporation, the company declares how many shares are authorized for sale, and an initial selling price (called "par" value). For example, the company may "authorize" sale of 10 million shares at $15.00 par value. This means that the company is making allowances to raise $150 Million. This money will go right into the company bank account. In exchange, the people who buy the shares become proportional owners of the corporation, as shareholders.
Once shares have been initially sold by the company, they can later be "traded" on the open market, like the New York Stock Exchange. The company doesn't receive any further cash, because it is the shareholder who is selling the shares, not the company.
Your question relates to the company raising "additional" capital. They can do this in either of two ways.
1) If the company never sold all 10 million shares to begin with, they can sell the remaining shares that they still hold. Thus, if they only sold 5 million originally, they can sell the other 5 million pretty much without further ado.
2) If all the original shares HAVE been sold, then they would have to amend the Capitalization section of the Articles of Incorporation, to authorize sale of new shares. This would require approval by a majority of existing shareholders. The reason for this is because raising more capital - in essence selling more of the company to outside investors, DILUTES the ownership portion of existing shareholders.
Example: Let's say that the person with the most shares of ABC Corp owns 2 million shares (of total 10 million). This person owns 20% of ABC Corp. Now if ABC issues 10 million NEW shares, then there will be a total of 20 million outstanding shares, and the same person will now only own 10% of ABC Corp. Thus, he/she will have less influence over the direction of the company. In some cases, existing shareholders have "first dibs" on new stock issuance, to maintain their existing ownership ratio.
Anyways, the bottom line is this, the company needs money to stay in business. The money may be needed for building leases, payroll, employee benefits, debt payments, and the like. By selling more shares to new investors, it raises the money it needs without having to find new customers or bring on more DEBT. However, it now has more shareholders to deal with, who want quarterly dividends, growth in the value of the shares (for resale on the stock exchange), and/or a say in company policy.
Very complicated stuff, but also very interesting. Hope this helps you understand.
4 years of law school.