The definition of a wide economic moat is essentially a type of sustainable (long term) competitive advantage that a company possesses which makes it difficult for competitors to steal market share or earnings.
Economic theory states that in a competitive market, a profitable niche will always bring in competitors that are able to eat market share and chip away at excess profits. Increased competition makes it difficult for a company to consistently grow earnings and profits unless they are able to maintain an advantage. This advantage could literally be anything from a patent, operations efficiency, brand recognition (KO) or just pure economies of scale (WMT, GE).
Knowing this, we can easily see the role of this principle. Dividend growth investing is predicated on long term growth by investing in companies that are continually improving earnings and dividends as a result. In this Darwinian economic world companies are always competing to survive. An economic moat minimizes risk and vulnerability to changes in underlying fundamentals of an investment, especially during a weak economy.