In ordinary induction you prove n+1 using n but in strong induction you prove n using all k<n. So for example, we will prove every number n>=2 is a product of prime. Suppose it is true for all k<n we will prove it is true for n. If n is prime proof complete. Otherwise n=p*q where p,q<n but by strong induction p and q are a product of primes, so n is a product of primes.