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?