Repeat, iterate, reiterate, ingeminate can all mean to say again.
Repeat, the word in ordinary use, may apply to what is said or uttered or done again, whether once or many or an indefinite number of times.
Repeat sometimes implies a change in the speaker or doer.
Iterate usually implies one repetition after another, especially of something that is said. There is very little difference between iterate and reiterate, except that iterate occasionally refers to a second saying or uttering or sometimes doing and reiterate carries an even more emphatic implication of manifold repetitions; consequently the two words are often used together when insistency is implied.
When only one term is desired to make this point, reiterate is especially appropriate.
Ingeminate, a somewhat uncommon term, implies reiteration for special emphasis or impressiveness. It therefore seldom implies indefinite repetition but rather duplication or triplication for the sake of the effect produced.