GIS datasets can be broken down into two types: raster and vector.
Raster datasets are anything with pixels. Raster datasets include things like aerial photos, DEMs, vegetation classification, and satellite imagery. There are also several different types of raster data, including ESRI grids, ERDAS Imagine files (.img), geotiffs (.tiff), MRSIDs (.sid), and geodatabase raster datasets.
Vector datasets are points, lines, or polygons. Vectors datasets including things like towns, streams, lakes, or anything else that can be a point, line, or polygon. There are several types of vector data, such as shapefiles and feature classes (in geodatabases).