Microsoft Project is a project management software that allows users to plan projects by defining tasks, assigning resources and timelines, tracking progress, and analyzing workloads and budgets. It was initially created internally at Microsoft in 1984 to help manage their large number of software projects. Key features include creating Gantt charts, critical path schedules, assigning resources to tasks, and monitoring project progress against the original plan. Crashing allows expediting schedules by compressing durations but at increased costs, with the goal of minimizing time while controlling additional expenses.