Key signature
A key signature is the sharps or flats written at the start of the staff, right after the clef. They apply to the whole piece, in every octave, and tell you the key of the music.
Instead of writing a sharp before every F, it is written once, on the F line after the clef, and every F in the piece, high or low, is F♯ even though there is no sign by the note. A natural sign cancels the key signature for one note.
The signs show the key. No signs: C major or A minor. One sharp, F♯: G major or E minor. One flat, B♭: F major or D minor. A major key and its relative minor share the same key signature.
Sharps in a key signature always appear in a fixed order, F C G D A E B; flats in the reverse order, B E A D G C F. Read the key signature first, before you play the first note.
What it sounds like
With F♯ the scale sounds like a proper major scale, with a half step as the last step into G. Without the sharp, the seventh note would sound out of place.
Where it is taught: the studio’s interactive textbook, chapter 7, “G and F major: key signatures” and chapter 8, “Minor: A minor and relative keys”.