An interval is a measured distance. It could be in time or distance. In music it usually refers to the distance between the natural notes or the white keys on a piano.
Unlike most intervals, in music you include both ends as part of the count. For instance, you play a C and an E. You would calculate the distance beginning on C and then step to D and end on E: C-D-E and it would be a 3rd interval. if you went from C and went all the way up to A, it would be a 6th interval: C-D-E-F-G-A. It's possible to modulate the intervals into ones referred to as: Perfect, Major, minor, diminished and Augmented and rules to figure each one apply. But, the fundamental interval is just measuring how many white keys does it take to get from the first note to the last.
If you have an interval, you have 2 ends with a note letter representing each one, like: C-E. If you have 2 notes you can play them in 2 ways: together or separately. If you play your notes 1 at a time it is a Melodic Interval - like you sing a Melody, one note at a time. If you play your notes at the same time then it is a Harmonic Interval - like when you add notes to the Melody and play more than one note at a time, adding some Harmony.
But really, an interval is just the measurement from 1 white key to another, like 1 inch or 1 foot.