A Sharepoint Feature is a functional component that can be activated and deactivate at various scopes throughout a Sharepoint instances, such as at the farm, site collection, web, etc. Features have their own receiver architecture, which allow you to trap events such as when a feature is installing, uninstalling, activated, or deactivated. They are helpful because they allow ease of upgrades and versioning.
The two files that are used to define a feature are the feature.xml and manifest file. The feature XML file defines the actual feature and will make Sharepoint aware of the installed feature. The manifest file contains details about the feature such as functionality.