A standard minor chord can be composed of the root of the minor scale, the third of the minor scale, and the fifth of the minor scale. In the key of Am, for example, those notes are A, C, and E. If, instead of the fifth of the minor scale you take the diminished fifth – the one that is half-step lower than the fifth, you will get a "diminished chord", which is also known as a "diminished triad". The diminished Am chord, for example, is A, C, Eb.
A diminished chord, also known as a "diminished triad", is composed of three notes where there are one-and-a-half steps (three semitones) between the first and the second note and one-and-a-half steps between the second and the third note.
Another way to say this is to say that the chord is composed of a minor third (the one-and-a-half steps between A and C in the above example) and another minor third (the one-and-a-half steps between C and Eb in the example). Alternatively as above, you say that the chord is composed of a root, a minor third, and a diminished fifth.
The chord uses many notations, such as Adim, Am(b5), A-(b5), or A-.
What is interesting about the diminished chord is that it is considered dissonant or atonal as it lacks a tonal center. The diminished Adim chord as above is A, C, Eb. At the same time, the dominant seventh chord built on F is F, A, C, Eb. Finally, the diminished Adim itself occurs naturally in the major scale in Bb. The chord is dissonant as it is hard to figure out what scale it belongs to and what tonal center it drives to.