Trello is a free online collaboration tool that allows users to organize projects and tasks into boards, lists, and cards. It provides a visual way to see projects unfold through different stages by dragging cards across lists. The tutorial explains how to set up a Trello board to organize tasks for an upcoming trip to Palawan, including creating the board, adding lists like "To Do" and "Doing", and populating lists with cards for individual tasks. Trello provides a flexible way to track progress on projects and share updates with others.