I have heard many versions of people defining Agile development. I met someone who claimed that they use Agile development in their project. When asked how can they say they are doing Agile development, it was told that team meets in the morning everyday to discuss status and hence the project is using Agile development.
I have also heard people talking about Agile development in a manner that it will automatically solve all your development problem, they do not realize if not implemented properly, Agile development methodologies can actually backfire. Others confuse Scrum with Agile development, well they are not completely wrong, but one needs to realize Scrum is a Agile Framework like Kanban, Extreme Programming, SAFe etc.
Keeping it simple, lets take a quick look at Agile manifesto.
Individuals and interactions over processes and tools
Working software over comprehensive documentation
Customer collaboration over contract negotiation
Responding to change over following a plan
And then 12 principles
We are talking about focus on customer satisfaction, continuous delivery, accommodate changing requirements, frequent collaboration between Business and development teams, focus on people than on processes, more focus on face to face and frequent interactions, focus on working software, reflect on current processes frequently and self improvements.
One thing to note is Agile development methodologies or manifesto nowhere gives a series of steps or rules. These are guidelines, which one need to apply to ones project. This will definitely help but there is no silver bullet. There are Agile frameworks and methodologies as mentioned above, but you still need to figure out what will work for you rather than blindly following some document or advice of a so called expert. Best way is to look at as many methodologies and frameworks as possible, pick up the practices which you feel will work for you, and keep on validation after a short period what is working and what does not.