Second
A second is an interval of two letter names: two neighbouring notes, such as C and D. It comes in two sizes, minor (a half step) and major (a whole step).
A second is made of neighbours. From C to D there are two letter names, both ends included, so C–D is a second. A scale moves in seconds: every step of a scale is one.
Seconds come in two sizes. A major second is a whole step, two half steps: C–D, D–E, F–G. A minor second is a half step: E–F and B–C, which have no black key between them, and also C–D♭. In the C major scale five seconds are major and two are minor.
On the staff a second is easy to spot: one note on a line, the other in the next space. When the two sound together they are too close to stack, so the heads are written side by side. In “Happy Birthday”, the melody rises a major second on “Birth-”.
What it sounds like
A second sounds close and tense: the two notes seem to rub against each other. A minor second is sharper still than a major one.
Where it is taught: the studio’s interactive textbook, chapter 15, “Intervals: unison to octave”.