A diad is any two notes played simultaneously. They don't have the harmonic completeness of a triad but still contain enough harmonic structure to have a tonal context. They can be used in any style in everything from substitution for chords and passing tones to lead playing and riffs.
Let's take a look at a harmonised diad progression in A Major. If that sounds confusing it means a progression through a scale of A major using groups of two notes in a logical, harmonic order. Looking at the music diagram you can see all the pairs of notes. Those are diads.
When playing this on piano play your way through using the same two fingers the entire way through (probably your thumb and first finger, or first and second fingers, but other combinations are also recommended to expand your playing skills). To play this on guitar fret with your first finger only the entire way through, with obvious exception of the second last diad which occurs at the twelfth fret. You'll need your first and second fingers for that. You could also play this through with your first and second finger, or second and third. Which ever instrument you play make sure you play it reverse order too - descending.
You might also look at this and think, "wait! The lowest note here is an E-note. Aren't we playing in E. And therefore those are 4th diads." No. The D note which occurs helps define this as an A Major progression plus the lack of a D#/Eb which would occur if we were in E. The root note is the A note in the first diad, the E note paired with it is an inverted 5th. And on the progression continues following that formula. The higher set of notes is simply an A Major scale (upper notes in the music score, G string in the guitar tablature).
How to use them? That's for another time, but the first paragraph in this post gave a few ideas.