A partition is a division of either your internal storage or your sdcard.
Internal storage of Android devices is devided into several partitions, each dedicated to a special "task". Some of the more important ones include:
/system: This is where the Android system and the pre-installed apps reside. It usually is mounted read-only, so on non-rooted devices you cannot write here (with the exception of applying a system update, e.g. OTA, or flashing a new ROM)
/data: Here the downloaded apps and all app's data are located. Additionally, some system settings are stored here, log files, and more
Your sdcard usually has a single partition only -- but also could be split into multiple partitions. The latter is mostly done for things like App2SD+ or Link2SD, which provide extended features for moving apps, data and caches from the internal storage to sdcard.
For more details on partitions, you might want to visit Wikipedia.
- SD card partitioning? why? how?
- How can I view the Android internal partition table?
- What is system partition? How its size is fixed? Can it be resized?
- Creating App and Swap partition for Android
- Android Partitions Explained: boot, system, recovery, data, cache & misc (AddictiveTips)
- How To Backup Your Android Phone’s Boot, Recovery And System Partition Images (AddictiveTips)