Look at the fingerboard on the piano and use only white keys. Identify C (to the left of the 2 black keys) and we'll call that 1.
Now each white key afterwards we'll assign the next number, D=2, E=3, and we get this in 1 octave:
C D E F G A B C
1 2 3 4 5 6 7 8
This makes up a C major scale in 1 octave (or 8 notes):
Let's examine what makes this a major scale. Notice the black keys sitting in between some of the white keys? Every closest move you can make on the keyboard is a half-step, and if 2 halves make a whole, we can figure this out.
Notice between C and D is 2 half steps (H), or a whole step (W), and continue:
C-D = W (1-2)
D-E = W (2-3)
E-F = H (3-4)
F-G = W (4-5)
G-A = W (5-6)
A-B = W (6-7)
B-C = H (7-8)
It is the distance between the notes that give any scale its particular sound. BTW, memorizing the W,W,H,W,W,W,H will allow you to easily learn all 12 major scales.
Once you understand this, please move on to the modes section.