Flat
A flat (♭) is a sign that lowers a note by a half step: one key down, to the left. A flat before E turns it into E♭.
In written music the flat stands right in front of the note, on the same line or space, and applies to that note until the end of the measure. A flat written right after the clef is part of the key signature and applies to the whole piece, in every octave. One flat in the key signature, B♭, means F major (or D minor).
Most flats lead to a black key: D♭, E♭, G♭, A♭, B♭. Each black key also has a sharp name, so E♭ is the same key as D♯; which name you see depends on the key of the music. In Lithuanian and German letter names B♭ is written simply B, and B natural is H.
From F and C a flat leads to a white key: F♭ sounds as E, C♭ as B. A flat is cancelled by a natural sign.
What it sounds like
A flattened note sounds just slightly lower than the plain one, by a half step. E and E♭ differ by the smallest step there is.
Where it is taught: the studio’s interactive textbook, chapter 5, “Half steps, whole steps and the black keys”.