A tuning system (commonly referred to as a tuning) is a set of pitches used in one's music. In other words, it is the decision of what fundamental frequencies the notes of instruments will be "tuned to."
Most musicians in the western world are familiar with only one tuning, a tuning called 12-tone equal temperament, where the interval of the octave is divided into twelve equally spaced notes. There are, however, an infinite number of possible tunings, each tuning resulting in different musical possibilities and characteristics.
There are many schools of thought regarding what tunings are most useful and how those tunings should be generated. With each of those perspectives comes a different system for generating tunings. Some of the most common systems are just intonation, regular temperaments, circulating temperaments, and equal divisions. Another source of tunings is those used historically and by various cultures throughout the world. Some of those tunings include Indonesian Pelog and Slendro, the Indian Shruti, Middle Eastern Maqamat, and Historical Meantone Tunings.