[cheeseprocedure]

These tools let you focus on the bigger picture instead of the nitty-gritty.

Docker and Vagrant are convenient for building (and distributing) consistent environments on top of (potentially wildly) different software or hardware platforms. Docker has a ton of other tricks up its sleeve (one example is "layers:" http://docs.docker.io/en/latest/terms/layer/).

Chef/Puppet/Salt/et al. are configuration management tools which enable programmatic definition of infrastructure. The key point is: you define how the system should look, not the specific steps on how to get there. Abstraction layers (management of files/users/packages/services/etc.) provided by the CM tool shield you from a nightmare of permutations, corner cases, and platform-specific options; it'll just enforce a given configuration regardless of local changes.

Having a central source of truth for systems configuration is a gamechanger in itself; your configuration directives or applications can query (or update) your configuration management database, which enables some very cool automation with very little effort. Then there's the community: for any given stack, there's probably a well-documented, well-tested Chef cookbook or Puppet manifest to build it, instantly plugging you into a rich experience base.

Yes, one could script all of this from scratch, but I'm not sure why one would.