I was writing my post on distribution habits and change, and I realized that I some elaboration on the concept of package management was probably in order. This is that elaboration.
Most linux--and indeed UNIX, at this point--systems have some kind of package management:
Rather than provide an operating as one-monolithic and unchanging set of files, distributions with package management provide systems with some sort of database, and common binary file format that allows users to install (and install) all software in a clear/standardized/common manner. All software in a Linux system (generally) is thus, covered by these package managers, which also do things like tracking the way that some packages depend on other packages, and making sure that the latest versions of a package are installed.
The issue, is that there are lots of different ways to address the above "problem space," and a lot of different goals that operating system designers have when designing package management and selecting packages. For instance: how do we integrate programs into the rest of our system? Should we err on the side of the cutting edge, or err on the side of stability? Do we edit software to tailor it to our system/users or provide more faithful copies of "upstream sources"? These are all questions that operating system/distribution/package managers must address in some way, and figuring out how a giving Linux distribution deals with this is, I think, key to figuring out which system is the best for you, though to be fair, it's an incredibly hard set of questions to answer.
The thing about package management, is that whatever ideologies you choose with regards to what tools you use, what packages to include and how to maintain packages, the following is true: all software should be managed by the package management tools without exception. Otherwise, it becomes frighteningly easy for new versions of software to "break" old non-managed versions of a piece of software with overlapping file names, by overwriting or deleting old files, by loading one version of a program when you mean to load another version, by making it nearly impossible to remove all remnants of an old piece of software, and so forth, or just by making it hard to know when a piece of software needs to be updated to a new version for security fixes or some such.
I hope that helps.