Geographic information systems (GIS) are used in a wide range of academic and applied fields. Simply put, GIS allows you to combine tabular data (e.g. spreadsheet sheet) with a geographic boundaries (e.g. maps).
QGIS (or Quantum GIS) is an open source geographic information system, meaning that it can be downloaded and installed on your desktop free of charge. It runs on Windows, Mac OS X, and Linux. There are also numerous plug-ins that extend the functionality of QGIS.
Geocode: To create points on a map from street addresses in spreadsheet form
Overlay: To superimpose two or more maps or layers in the same coordinate system, to show the relationships between them
Georeference: To align geographic data (map, layer, etc.) with a given coordinate system, allowing for overlays
Select by location (proximity analysis): To select features according to their relationship in space to other features
Select by attribute: To select features according to their properties (attributes), like querying a database
Buffer: To create a zone around a feature in units of distance or time
Network analysis: To find the distance from a feature travelled along a network (such as roads, public transit) rather than as the crow flies
Join: To attach fields from one table to those of another through an attribute or field common to both tables.
Viewshed analysis: To determine what areas are visible from a particular location.
Adapted from Esri's GIS Dictionary.