When buying stock, what does it mean when it says a company doesn't pay dividends?

Does it simply mean that any gains are added to the original investment? Can those gains be realized by simply selling the stock?

Yes that is what it means.

Those gains are referred to as "Capital Gains"

For GROWTH companies you actually should prefer that they DONT pay a dividend. They should reinvest that money internally and get a better return on it funding more growth in the company. And since share price is typcially related to earnings growth you will see more Captial Gains with higher growth rates.

But when the growth slows you should want them to pay a dividend so you can inviest the gains how you want.

Assuming that the company makes profits, it means that they do not pay part of the profits to shareholders as dividends, but that they keep the profits in the company. Normally this is done if the company has a business that is growing, so they can use the profits to fund the growth. The profits stay in the company and can not be realized. If the retaining profits is seen by the markets as sensible behavior, this should reflect in increasing share prices, and this way you are getting richer.

You buy stock in a company for two reasons: to realize dividends, which the company pays out of its earnings, and to realize gains as the stock becomes more valuable. Some companies do not pay dividends, but re-invest earnings in the business in the hopes of increasing the company's worth. This is particularly the case with high-technology companies in the early stages of their growth, where re-investment to increase the company's business is important.

It means that all the profits, if any, are retained by the company in their reserves, to expand the business, or to pay off loans, etc. Be careful of such companies.

When a company produces their net income they have two choices. They either reinvest the income back into the company's operations or they pay the cash out as dividends to the shareholders. If there is no dividend then they are probably doing the the first. The income would sit on the balance sheet as cash. As a shareholder you would not realize any gains unless a dividend is paid or if the company uses the cash to buy back their own shares. Generally growing companies reinvest dividends (Google) into their operations while more mature companies will pay out the dividends (Phillip Morris).