Definition of ROI
Most simply, the return on investment (ROI) of a project is how much income is generated after subtracting the costs of the project.
Of course, in the real-world ROI is much harder to calculate. This is because the time that a project generates income can stretch over many years. For example, an ecommerce site might take 6 months to build, but will generate sales for years afterwards. Also, sometimes projects have only indirect impacts on income. An example of this is a new customer service system. Everyone knows that customer service is important so building a system to improve on the level of service can be a good idea. But since the customer service team doesn't actually sell anything, how do you measure the bottom-line impact of a project?
I've also put together a description of project management fundamentals if you're interested in learning more about this profession.