Numeric data is statistical data which includes a geographical component or field that can be joined with vector files so the data can be queried and displayed as a layer on a map in a GIS. The most common type of numeric data is demographic data from the US Census.
Vector data is data that has a spatial component, or X,Y coordinates assigned to it. Vector files can contain sets of points, lines, or polygons that are referenced in a geographic space.
Raster data is data in a .JPG, .TIF, .GIF or similar format. Items scanned using a flatbed scanner like this map are examples of raster files. Images taken with a digital camera produce these same types of files.
Polygons (properties), lines (streets), points (trees) and raster images (air photo) are separate layers integrated into one map.
This is a schematic of the various types of layers that can be used in a GIS.