"To start a dialogue" means to begin a conversation or discussion with another person or group of people. It suggests the intention to engage in open and respectful communication to share ideas, opinions, or concerns. Full definition
By starting a dialogue with residents, the park district can bring its plans in line with the needs of the community, he said. (articles.chicagotribune.com)
Have you set up a viable way for them to experience your product or service and started a dialogue about how it might help them? (entrepreneur.com)
In this sense dating blogs are a first step in starting a dialogue between readers and authors to swap dating stories and address issues of concern. (articlesfactory.com)