Korean is the official language of North Korea. It has slight variations, compared to the Korean spoken in the south, due to the isolation from a lot of the outside world after the end of the Korean War.
If you have learnt Korean in South Korea, you will be able to have conversations with absolutely no problem. The main difference appears with the level of formality and some vocabulary words. North Korean is much more formal than in the south. In fact, the way the people in South Korea speak can sound quite rude in some contexts in North Korea, so if you are a Korean speaker then use the politest version of grammar you can think of. A good example of this is to use the term jonun instead of nanun to refer to yourself.
Uniquely Northern
There are somethings that are now uniquely North Korean, such as the way you address other people. Usually, people will use the term comrade or dongji in Korean. This is used if the person is equal to or older than you in age. If they are younger then you can use the term dongmu.
The name of what you call the Korean Language and Korea is also different. In the south, the term hangul is used to refer to the language and hanguk is used to refer to Korea. In the North, however, you will always call the language chosangul and the name of the country is chosun. There are a lot of different arguments where these terms come from, but it is generally agreed that chosun refers to the time of a unified Korea under the Chosun Dynasty, whereas, Hanguk refers to a period called SamHan or 'three kingdoms'. This rule applies to many items in Korean culture that have the word han- in front. For example, the name of the traditional Korea dress in the south is called the Hanbok, but in the north it is called Chosun-ot.
Loan words
The two dialects have a major difference in vocabulary used. As the South has been much more exposed to the West there are more terms borrowed in English. Many of these words don't have an equivalent in the north. It is said that North Korean is possibly closer to a more pure Korean due to less English loan words.
Cultural effects
The linguistic and cultural differences between the two Koreas is also evident in folk songs that are known by both sides. One of the most famous songs on the Korean peninsula is called "arirang". The main parts of the song are all still the same however, certain verses have been changed. The North Korean version has specific references to the sacred Mount Paektu whereas the southern version does not.