To me, there is one major type of potential benefit and one major type of potential risk when a business diversifies.
The major possibility of benefit is that the business can increase profit and revenue. If a business, for example, diversifies up and down its supply chain, it can give itself (through vertical integration) advantages over competitors who lack such diversification. In addition, the business can hedge against problems in one area of business by having many different types of enterprises.
The problem, though, is that diversification can move a firm away from its core competencies. Firms that are good at one thing may not be any good at some other thing. When they branch out to go outside of the things they are truly good at, they become inefficient and actually lose profit.
So there is a risk/reward element in diversification. It can be profitable, but it can also harm a firm.