This is really simple.
A quadratic form ax^2+bxy+cy^2 is called "primitive" if a,b,c are relatively prime.
A primitive positive definite form is said to be reduced if:
|b| <= a <= c and b=>0 if either |b|=a or a=c. (where "<=" indicates a non-strict inequality).
So how can a,b,c be relatively prime, and then we say |b|=a or a=c?