It's Worldwide
Pentatonic scales are used in many types of music all over the world. Many different types of folk music use this scale. If fact most people are familiar with this scale without even knowing it because it's used so often. There's a great clip by Bobby McFerrin who sings a pentatonic melody to an audience and to their surprise, they finish the tune without him! African and European (Celtic, Scottish, Russian) folk music use pentatonics quite frequently.
It's Only 5 Notes
Most beginning musicians are familiar with only the minor pentatonic scale. In fact there are many different types. There is one based on the major scale, one on the minor, and many variations of these two. Basically a pentatonic can be defined as a scale with 5 notes...and that's all. It can be any 5 notes. So you can see how many possible permutations there could be. Also, pentatonic scales can be applied in different ways over different chords to achieve different results. In fact the major and minor pentatonics are the exact same notes applied in different ways over different chord progressions. That said, it's important to think of them in their own right i.e. the C major and A minor and not the C major starting on a different note.(It's important to think of all of your scales in this way i.e. A minor or D dorian and not C major.)
The Basics
Ok, let's start with the basics and go from there. The major pentatonic scale is the major scale without the 4th and 7th notes of the scale. These notes create certain tensions. Some music textbooks call them 'avoid notes' since they can sound 'wrong' when played at the wrong time.* The major pentatonic doesn't have these notes.The major pentatonic has the root, 2nd, 3rd, 5th, and 6th. That's it! The relative minor uses the same notes but the relationships end up being different. The minor pentatonic has the root, minor 3rd, 4th, 5th, and flat 7th. It's the minor scale without the 2nd and the 6th. (It's interesting to note that it's the 2nd and the 6th that differentiates the natural minor from the dorian and phrygian scales.) The blues scale is built upon this minor pentatonic but adds the flat 5th (the 'blue' note).
* There are no 'wrong' notes in music. There is only the situation where you are playing notes and not getting the desired outcome or sound that you intended.
Uses
The pentatonic scales are used in many ways. Initially they were used mostly in folk music as a basis for the melody and improvisation on that melody. They started to get used in jazz and rock and are used in almost every genre of music these days. The use of the minor pentatonic in rock music has almost become ubiquitous whenever you hear a guitarist going for a solo. Listen to any classic rock and guaranteed it's the scale used for the riff and solos and often the melody itself. Also, both the major and minor may be used in a song. The melody for the song will use the major scale but then the riff or solo may use the minor pentatonic. This happens in everything from country to rock.
Other Uses
There are a couple of other ways the pentatonic scales are used. First of all, since a pentatonic scale is technically any 5 notes, there can be many different possibilities for combinations. There are a number of different pentatonic scales*, quite a few of which have exotic sounds (and names). There is: Balinese, Chinese, Egyptian, as well as variations like the pentatonic Scriabin was famous for (a major pentatonic with a flatted 2nd).
*This is the Dolmetsch music theory site. Enter root note and scale from drop down menus to get the notes from any scale on the list!
Then there are the application of the major and minor pentatonic scales over different chords and keys. For example in the key of C major you could use the C major pentatonic (A minor pentatonic). But you could also use other pentatonics like the E minor pentatonic or B minor pentatonic. Using these you end up playing different extensions over the chord. They can offer up some interesting sounds, especially when used in more elaborate chord progressions.
Start With The Basics
When teaching students how to improvise, I usually start with pentatonics. They're a great leaping off point for learning how to create phrases and exploring the musical thought process. By starting with a pentatonic scale over a basic chord progression, students find that improvising isn't the big mystery that they think it is. It's also easier to talk about (and actually hear) different ideas about phrasing, where to put your phrases and how to make a musical statement. It's easier to explain (and play!) question and answer (call and response) concepts. Once you get into the basics about how we create musical ideas, then you can get into some more advanced concepts such as motives, repetition, development, etc.
Explore The Possibilities
Even though there is only 5 notes, there is a world to explore in pentatonic scales. It's best to take them one at a time and see what can be done. Like everything else in music, it's better to know how to effectively use one scale, than it is to memorize a dozen without having a clue about how to use them. Take your time and explore the possibilities.