Point addition in affine coordinates involves the computation of modular inverses for elements of the underlying finite field. Modular inversion can be done with the extended Euclidean algorithm, although its cost is around 100 times the cost of a single addition or multiplication in the finite field.
Point addition in projective and Jacobian coordinates, however, don't require to compute any modular inverse. Hence, the cost of adding two elliptic curve points in projective or Jacobian coordinates is much smaller than in affine representation.