Hi Marielle,
I would agree that agile is a little bit of an abstract idea to wrap your head around especially if you are not practicing the methodology in your everyday work life. It helped me better when i was able to wrap my head around the fact that typical project plans before agile were very rigid and firm. All information related to the project are relatively fixed and known up front. A person building a modular home knows exactly how much material, labor, time etc they will need to build that same house over and over. They can then create a standard waterfall plan to say it will cost us $XYZ dollars and ABC days to complete your home. Here are the risk, here is the timeline, here are the cost. This is because this information and details are known at the star of a project.
I work in software implementation as a Project Manager . Our customers usually don't know all of their requirements at the start of the project. This means, it would be impossible to give a deadline (time) , a fixed value for materials, a fixed value for labor, etc. Because this is the case, AGILE works in checkpoints where priority is given to the most important task/deliverable that returns value to the customer. If I'm building a customers website for E-commerce sales with waterfall, I will know exactly how the site will be built and it associated risk. With AGILE I will build portions of the website as we go and more data or requirements are available to me. This usually means we have to meet more to extract this information (workshops, Check-ins, SCRUM) and prioritize action items, but since we meet more we don't document as much as a traditional project because the details are ever changing.
I'll be glad to help answer any additional questions as they relate to AGILE. I have been utilizing it as my primary form of Implementation Project Management for the last 7 years while working cooperatively with partners who implement with a traditional waterfall approach.