Why is regression important for the society in Ayn Rand's Anthem?
The society that Ayn Rand depicts in Anthem is one in which individual thought is condemned and all men must live for their brothers. The first sentence is "it is a sin to write this," because the narrator, Equality 7-2521, knows that writing means thinking for oneself and creating words only he will see. This is punishable by law.
I will assume that by "regression" you mean the act of moving backward; the opposite of forward progression. The society has regressed in many ways. Most noticeably, they have done away with electricity; when the narrator is writing in his diary, he has to use candle light that he has stolen. The leaders of the society value regression because it eliminates individual thought. They believe that the people from the "unmentionable times" (i.e. us, or the people from the reader's present) were evil because they abused their freedom and had too much power. We (the people of their past) had progressed too far, and they needed to go back to the "dark ages" in order to create a society which could be easily controlled.
By moving backward instead of forward, the leaders are able to stay in control. Individual thought and non-conformity, to them, is evil and dangerous, and advances in technology would encourage individual thought. Having certain technology available might allow people in the society to challenge the status quo, and things would go back to the way they were in the "unmentionable times," which, from the point of view of the leaders of the society, would be devastating to all.