The definition of a project in agile terms is no different to that of a project in traditional terms. The difference is how the project is run and executed and the values behind the project.
Both agile projects and traditional projects:
- have a start and end
- may be constrained by schedule, scope or budget
- should be for a single product; (lets not debate symantics)
- run internally built or by external vendors
- be part of a larger program or portfolio of work
- deliver a product
- deal with risk management and risk mitigation
- If you look at PRINCE2 and PMBoK, both promote iterative approaches in the form of stages or phases. Most agile frameworks do to.
Agile recognises that we deal with complex technologies and requirements in a world of many uncertainties and ambiguities. In doing this the approach is more an empirical process control instead of following a defined process control. It allows the team to adapt around challenges.
The work is done in very short iterations, not exceeding 30 days to mitigate risk against these complexities and uncertainties. Traditional projects may run for years without phases, or phases may be several months. Agile practitioners feel that this is far too long and far too many risks are involved.
Most Agile practices follow lean principles to eliminate waste and only build what is needed. Agile practitioners recognise upfront requirements normally lead to high volumes of waste; e.g. 64% of features are rarely or never used - Standish Group Research.
Most people don't get agile as it is hard. The reason it is hard is we have all been educated to work with defined processes and control these processes. Breaking this mindset to deal with and learn to manage complex projects using empirical process control takes a lot of energy and commitment. It has been proven to be a very reliable way to deal with software projects but needs the change.
I have done some pod-casts on project management and Scrum which highlights these differences in detail, you may want to use google to try find these.