Forward yield is a way to anticipate the upcoming dividends for the year based on the company's dividend history and your best guess at how it will perform in the future. Trailing yields, however, are based on solid historical data and are incredibly easy to verify and support.
Both are important when you're thinking about buying a stock. Forward dividend yield, when calculated based on the reality of the stock market and not on an optimistic view, can help you anticipate what you'll earn in the coming year. Trailing yields will tell you what's definitely already happened (and can help you figure out that forward yield).