As agile methods have spread in popularity in the early 2000s, one of their most obvious characteristics is their towards change. Before they appeared on the scene most of the thinking about software process was about understanding requirements early, signing off on these requirements, using the requirements as a basis for design, signing off on that, and then proceeding with construction. This is a plan-driven cycle, often referred to (usually with derision) as the waterfall approach. Such approaches look to minimize changes by doing extensive up-front work. Once the early work is done, changes cause significant problems. As a result such approaches run into trouble if requirements are changing, and requirements churn is a big problem for such processes.
A decade ago, database licensing costs could make individual database instances prohibitively expensive - but these days this is rarely the case, particularly as open-source databases have grown in popularity. We've found it handy to run a database in a virtual machine running on a developer's machine.
Agile processes approach change differently. They seek to embrace change, allowing changes to occur even late in a development project. Changes are controlled, but the attitude of the process is to enable change as much as possible. Partly this is in response to the inherent instability of requirements in many projects, partly it is to better support dynamic business environments by helping them change with the competitive pressures.