Agile is an iterative approach to project management and software development that helps teams deliver value to their customers faster and with fewer headaches. Instead of betting everything on a "big bang" launch, an agile team delivers work in small, but consumable, increments. Requirements, plans, and results are evaluated continuously so teams have a natural mechanism for responding to change quickly.
Proof of concept in software development is a controversial topic. The person that came up with a software idea is usually convinced of its relevance. And stakeholders usually don't want to spend time on something that is not even going to be included in the final product.