Cohiba cigars have a very interesting story regarding their name. The first mention of the name Cohiba dates from 1496, when Christopher Columbus visited the American Continent in his many trips. In one of such trips, he revisited Hispaniola, which was the name under which the Dominican Republic was known back then. He noticed that locals from the Taino tribe smoked leaves of cured tobacco. He asked the name of what seemed such a strange habit and the natives answered Cohiba.
More than five centuries later, Cohiba cigars are the modern equivalent of that habit that perplexed Columbus so much. There are two main brands, and although they share a common origin, they are now completely different in type, blend and size. There is a Cuban variety, which is unfortunately (for cigar lovers) forbidden in the United States of America, and there is a Dominican variety, which is the only type of Cohiba cigars that can be legally bought and consumed in the United States.
Nevertheless, there is a black market for Cuban Cohiba cigars in the United States. However, it is not very advisable to buy them as most of the time, they are just counterfeits. If you really want to try Cuban Cohiba cigars, your best bet is to get them in Canada. In theory, it is still illegal for Americans to buy them in Canada, although Canadian authorities would not stop Americans from buying them, claiming that such a law does not apply in Canadian territory. It is a bit riskier to try to bring them in the United States. I do not know what happens if they are found on you when you cross the border, but I advise you not to push your luck. There are also Cuban Cohiba cigars in Mexico, but most people industry agree that they are as counterfeit as the ones sold in the United States.
I would advise you to try Dominican Cohiba cigars instead. The flavor is different, but that does not mean it is worse. It is just that: different. On the other hand, you would not have any trouble getting your Cohiba cigars from the many authorized retailers in the United States. More over, since they are legal, there is not a risk to buy counterfeit Dominican Cohiba cigars. There is not a black market either where prices are inflated either. In addition, you would not need to travel all the way to Canada just to get a smoke.
In any case both Cuban and Dominican Cohiba cigars are valued by cigar connoisseurs all over the world.