Section One: Introduction
Currently owned and developed by the IBM corporation, SPSS stands for "Statistical Product and Service Solutions," and is primarily used for statistical analysis, as well as data mining, text analysis, and data collection.
In the past decade, the program has gone through several name changes. Originally, it was known simply as "SPSS." With the release of v. 17, the name was changed to "SPSS Statistics," and then again to "PASW Statistics" in v. 18, and yet again to "IBM SPSS Statistics" in v. 19, after SPSS Inc. was acquired by IBM in 2009.
When the program was first developed, it stood for "Statistical Package in the Social Sciences," although the change in the overall scope of the software's use necessitated the subsequent change in its label. 
The program itself is quite versatile, and provides many and various tools for data analysis, and has the ability to create reports and graphs from the data gathered. 
IBM SPSS is what is called a "modular product," requiring first the base system to run, with various other packages capable of being installed which can perform much more specialized types of analyses.  NCSU currently has licensing for the SPSS base client as well as the regression module and the advanced models module.
Software and licensing can be found at https://software.ncsu.edu/.
 Wagner, William E. Using IBM SPSS Statistics for Social Statistics and Research Methods. 4th ed. Thousand Oaks, Calif: SAGE, 2013.
 "SPSS," ITS, University of Southern California: www.usc.edu/its/stats/spss/
 "SPSS," ITS, University of Texas at Austin: www.utexas.edu/its/products/spss