The C major scale is the only major scale that can be played using just the white keys of the piano. That makes it handy for explaining major scales in general.
A piano has 88 keys and each pair of adjacent keys is separated by an interval of a half step. The C major scale begins and ends on C. Between C and D there is a black key. It is a half step above C and half step below D. That makes the interval between C and D a whole step. Similarly, these pairs of white keys are a whole step apart: D-E, F-G, G-A, and A-B. But two pairs of white keys in the C major scale have no black key between them: E-F, and B-C. They are each half step intervals.
So the C major scale has a specific pattern of whole steps (w) and half steps (h): w-w-h-w-w-w-h. In fact, a major scale starting on any key – white or black – has the same pattern of whole steps and half steps.
The piano keys correspond to the horizontal lines and spaces on a musical staff. This staff shows the C major scale with each note in the scale aligned directly below the same note on the piano keyboard. It is not obvious from looking at the score that the interval between C and D is different from the interval between E and F. It helps to have the image of the piano keyboard as a reminder of this.