Agile software development - An iterative and flexible approach to software development.
Scrum - One type of agile software development, where the basic unit of work is a sprint (see below).
Sprint - The regular work cycle of the scrum method. Most teams prefer short sprints of one-two weeks when all assign tasks can be completed.
Stand-up - A daily (usually morning) meeting to quickly get status updates on yesterday's completed and today's planned work. Standing helps avoid long drawn out meetings.
Scrum Master - A team member that helps facilitate the scrum process and assist in communicating and protecting the team from outside distractions.
Also to help give context to agile methodologies, defining an alternative may help:
Waterfall Model - A classic approach to software development that consists of rigid and sequential stages consisting of gathering requirements, designing, implementing, verifying, and maintaining software. This approach is generally criticized as being too rigid and slow to respond to the realities of customers and business needs.