We have investigated systematically the nature of counterion condensation on the uniformly charged flexible polyelectrolyte chain by monitoring the role of counterion valency, chain length, temperature, and dielectric constant through a Coulomb strength parameter, and volume of the system. Radius of gyration of the polymer, radial distribution functions of monomers and counterions, and formation of dipoles are also studied. Our simulations show that the essential features of counterion condensation for a flexible polyelectrolyte are qualitatively different from the Manning theory.