Division algorithm involves dividing a dividend by a divisor to obtain a quotient and remainder. There are two types of division algorithms: restoring division and non-restoring division. Non-restoring division was demonstrated by dividing 8 by 3 in binary form using a divisor of 0011, a minuend of 1000, and a running difference stored in a accumulator to iteratively obtain the quotient 1000 and keep the division process non-negative.