In music theory, a minor third is an interval that has three half steps
The minor third requires that:
- The interval must be a third interval (three note names between the first and the last).
- The interval must have three half steps.
What does a minor third look like?
Here is an example of a melodic minor third (two music notes in a melody) and a harmonic minor third (in a chord):

How to recognize a minor third?
Rule of music theory: All intervals in a major scale starting with the tonic (degree I) are either major or perfect, and only unison, octave, fourth and fifth are perfect (the others are major).
Example with the interval C / E♭ :
Let's take the C major scale to have C as the tonic:

From the rule stated above, the interval C / E♮ is a major third, so the interval C / E♭ is a minor third.
Inversion of the minor third
The inversion of the minor third is the major sixth.
Here is an example of a major sixth:

Musical examples of minor third
Guten abend, gute Nacht (lullaby) by Johannes Brahms
Johannes Brahms' lullaby (Guten abend, gute Nacht in German) has many minor thirds:

Greensleeves
The traditional English song Greensleeves has a many minor thirds:

Interval identification game
You will find this interval in my Intervals identification game: