Ubuntu's package management system is derived from the same system used by the Debian GNU/Linux distribution. The package files contain all of the necessary files, meta-data, and instructions to implement a particular functionality or software application on your Ubuntu computer.
Debian package files typically have the extension '.deb', and typically exist in repositories which are collections of packages found on various media, such as CD-ROM discs, or online. Packages are normally of the pre-compiled binary format; thus installation is quick and requires no compiling of software.
Many complex packages use the concept of dependencies. Dependencies are additional packages required by the principal package in order to function properly. For example, the speech synthesis package Festival depends upon the package festvox-kalpc16k, which is a package supplying one of the voices used by the application. In order for Festival to function, it and all of it's dependencies must be installed. The software management tools in Ubuntu will do this automatically.