To iterate is to repeat, as in to say or perform something again. If you loved the high school drama club’s performance of the “Three Little Pigs,” encourage them to iterate the musical so you can see it again. And again.
Iterate comes from the Latin word iterare for "do again, repeat.” Iterate is a transitive verb, so you have to iterate something. A successful play or concert will usually iterate a performance, so more people can see it. People often iterate a point, by repeating, they hope others will understand it better. Politicians often iterate key points. The word reiterate is more familiar, and means something very similar — to repeat something for emphasis.