If your broker doesn't allow fractional share trading, you would only be able to buy one share, and the additional $122 would remain in your brokerage account, uninvested. On the other hand, fractional share trading would allow you to use your entire $600 deposit to buy about 1.26 shares of Berkshire Hathaway stock.
Second, it allows investors with relatively small amounts of investable cash to buy whatever stock they want. As an example, MercadoLibre (MELI -1.72%) trades for about $1,300 per share as of this writing. Unless you have that much cash available, you can't afford to buy any shares if your broker doesn't allow fractional shares. However, if they do allow fractional share investing, you could add MercadoLibre shares to your portfolio for as little as a few dollars.
Should you use fractional shares to invest?
The short answer is that you should absolutely use fractional shares to invest if they're available to you. Not all brokers allow fractional share trading, so if you're a new investor or you simply want the ability to buy less than one full share of stock on occasion, it may be a good idea to find a broker that supports fractional share trading.