We should note first of all that not all business interests were in favor of this war. For example, Andrew Carnegie was a major leader of the anti-imperialist cause. In fact, people like Theodore Roosevelt who were strongly in favor of the war were not at all happy with the business community who, they thought, did not support the war strongly enough.
However, there were business leaders who did want a war of conquest. These leaders felt that securing Cuba would be good for business. American companies had about $50 million invested in Cuba and did $100 billion in trade with the island each year (source: Bailey, Kennedy, and Cohen, The American Pageant 11th edition page 646). Businesses that had an interest in the island felt that their interests could be better protected if Spain were ejected and the rebellion in Cuba ended.
In addition, there were those who wanted an empire beyond Cuba. They felt that it was important to give American businesses new markets to sell to and to get raw materials from.