The tenor guitar is a slightly smaller, four-string version of the steel-string acoustic guitar or electric guitar. The instrument (in its acoustic form) was developed so that players of the four-string, tenor banjo could double on the guitar. Later, solid-body electric models were also produced.
Traditionally, tenor guitars were tuned like tenor banjos, that is, in fifths like a mandolin. From low to high: C G D A.
Like many things, you can have all sorts of different tunings. Celtic (Irish) musicians favor G D A E tuning (and that makes me wonder that the reason there are six tuning pegs is so that you can use different sets of strings…). Ani DiFranco uses all sorts of alternately tuned tenor guitar in her songs.