Since Linux is just the Kernel, you can't do much without additional tools. A shell is necessary to let the user type commands. More tools are required to let him manipulate the FileSystem and edit files. Most every task requires a program to be installed. Building a LinuxDistribution means choosing which tools to include for which tasks, and configuring them all to work with each other out of the box as far as possible. Nowadays, a LinuxDistribution is usually equivalent to a large collection of Packages.
Old PCs with slow CPUs, little RAM and small HardDisks may not be able satisfactorily run the mainsteam distributions listed above. There are specific distributions designed to run on such limited hardware; of course, they have to omit features and applications to achieve their goal.
Some LinuxDistributions can be booted from removable media such as a FloppyDisk, a LiveCD, or a KeyDrive and don't require installation (or indeed any kind of write access at all) to HardDisk. Such a media provides both an excellent way to try out a LinuxDistribution without having to change your Partitions as well as a great tool platform for things like network diagnosis and system repair (be it for Linux or other OperatingSystems).
A cuckoo is a bird that lays its eggs in another bird's nest. In a similar manner, some LinuxDistributions can be installed to HardDisk into another OperatingSystem's Partition, without affecting the host system. This is usually achieved by means of storing image files in the host Partition to contain the Linux FileSystems.