The phrase "resounding majority" refers to a large and clear majority. It means that a group or a decision has won by a significant margin over the opposing side. Full definition
New York Times / Siena Poll Shows Resounding Majority of New York City Voters Want More Public Charter Schools (necharters.org)
«When people are asked on surveys whether they care about how an animal was treated,» he says, «the resounding majority claim they do. (canadianbusiness.com)
Even though he was elected Leader of the Labour Party with the support of a resounding majority of Labour members and supporters, it is now clear that Corbyn can not fulfil the most important aspect of his job: the role of Leader of the Opposition. (democraticaudit.com)