Here is a super-brief explanation of shapefiles:
1. Shapefiles contain geographic elements: either points, lines, or polygons.
Points might represent tiny local objects like fire hydrants.
Line-files are used to show linear things like roads, streams, powerlines.
Polygon-files are used to show things with surface area, like Census Tracts and whole counties.
Since all of these elements exist “in three-dimensional space,” they are often called spatial elements.
2. Each entity in a shapefile has an identifier tag, and it is linked to a database table where one of the columns is the same identifier tag. In this database, different features that might be associated with the spatial element are called attributes or, more specifically, spatial attributes. For instance, a Census Tract can be represented as a polygon, and that polygon (that spatial element) can have various attributes like the total population, the population of African-Americans, of Latinos, of Asians, of non-Hispanic Whites–in other words, we could take all the Tract-level Census data we collect and add it to the attribute table (the database) of the shapefile, so that we can do things like create maps based on the relative concentration of one ethnic group or another in the Census-Tracts of our county.