Spatial (or geospatial) data is suitable for use in GIS mapping software (like ArcGIS or Google Earth) and can come in a variety of formats: vector, raster, or data tables.
Here's a list of new books at Columbia Libraries on using GIS.
In addition to the GeoData portal listed below, there are some tools to work with NYC spatial data without downloading a dataset and manipulating it with GIS. Here are a few examples:
Find spatial data using Columbia University Libraries' GeoData Portal (beta)!