A pentatonic scale
is just a scale made up of five
distinct notes. Any five notes will do, like C, C#, D, D#, and E, but the word "pentatonic" usually connotes a scale related to the Western major
modes. So a C (major) pentatonic would be C, D, E, G, and A, outlining a full C Major scale, but with a slightly different quality. You can rearrange these particular notes to form an A Minor pentatonic scale - A, C, D, E, and G, analogous to Western tradition that says A Minor is the relative minor to C Major.
Pentatonic scales are usually associated with folk musics from around the world, and "simple" melodies, since, after all, you're using a scale with fewer notes to worry about. But if those melodies were that simple, we could all be Albert King or Nusrat Fateh Ali Khan in Ten Easy Lessons. The blues is roughly based on the pentatonic scale, but you have a multitude of inflections that provides a universe of complexity.
In jazz, the use of pentatonics became widespread in the 1960s; it provided a "something new" in the melodic arsenals of improvisors as the harmonic basis of the music moved away from the bebop tradition. But in this case, it wasn't a matter of simply improvising, say, a D Minor pentatonic melody over the pianist's D Minor chord. The ambiguous neither-major-nor-minor chords in Herbie Hancock's "Maiden Voyage", for instance, could be handled with a major pentatonic scale that began a whole step below the root of the chord - i.e., an E-flat scale against an F9sus4 chord (F, B-flat, E-flat, G). An improvisor became free to use any of the twelve possible scales in any context, as long as it sounded OK; some uses, like the use of a major pentatonic scale a tritone below the root of an altered dominant wasn't far removed from the bop tradition.