Natural notes without the slide
In C, the no-slide notes already cover the C major scale. Blow notes are C, E, G, and C. Draw notes fill in D, F, A, and B.
Accidentals with the slide
Pressing the slide supplies the chromatic notes between the natural notes: C#, D#, F#, G#, and A#. These are the same pitches as Db, Eb, Gb, Ab, and Bb.
Why C is still useful after you change keys
Even when you play in G, F, Bb, or another key, the physical layout is still the C instrument layout. Learning the C map gives every scale a fixed address.