It's a typo. Clearly x^2-1 is always reducible as (x+1)(x-1).

The second part is talking about -1 being a quadratic residue modulo p, ie, does there exist an x with x^2 = -1 (mod p)? For example, -1 is a quadratic residue mod 5 and 13 (since 2^2 = -1 (mod 5) and 5^2 = -1 (mod 13)).

In general, if p is an odd prime, then -1 is a quadratic residue mod p if and only if p = 1 (mod 4).