Agile and Waterfall are two distinct methods of project management.
The Waterfall model can essentially be described as a linear model of project development. Like its name suggests, waterfall employs a sequential process. Development flows sequentially from start point to end point, with several different stages: Conception, Initiation, Analysis, Design, Construction, Testing, Implementation, and Maintenance.
In contrast, the Agile method proposes an incremental and iterative approach to project development. It was essentially developed in response to the limitations of Waterfall, as a way to give more freedom. The process is broken into individual models that team work on. There is no pre-determined course of action or plan with the Agile method. Rather, team-mates are free to respond to changes in requirements as they arise and make changes as the project progresses. Agile is a pretty new player to the development management. However, it has made substantial gains in use and popularity in the last couple of years.