Partitioning your disk simply refers to the act of breaking up your disk into sections. Each section is then independent of the others. It's roughly equivalent to putting up walls inside a house; if you add furniture to one room it doesn't affect any other room.
If you already have an operating system on your system which uses the whole disk and you want to stick Debian on the same disk, you will need to repartition it. Debian requires its own hard disk partitions. It cannot be installed on Windows or Mac OS X partitions. It may be able to share some partitions with other Unix systems, but that's not covered here. At the very least you will need a dedicated partition for the Debian root filesystem.
You can find information about your current partition setup by using a partitioning tool for your current operating system. Partitioning tools always provide a way to show existing partitions without making changes.
In general, changing a partition with a file system already on it will destroy any information there. Thus you should always make backups before doing any repartitioning. Using the analogy of the house, you would probably want to move all the furniture out of the way before moving a wall or you risk destroying it.
Several modern operating systems offer the ability to move and resize certain existing partitions without destroying their contents. This allows making space for additional partitions without losing existing data. Even though this works quite well in most cases, making changes to the partitioning of a disk is an inherently dangerous action and should only be done after having made a full backup of all data.