Minsk is the capital of Belarus and a very large city with almost 2 million people, so you can expect the attractions of any big city. One thing that makes Minsk unusual is its modern architecture. Although in its origin it's an old city - going back at least to the early middle ages - most of the city was destroyed in the Second World War and then rebuilt according to Stalinist principles. It is therefore of great interest to historians and people wanting to find out more about the Soviet era.
Apart from this there are still some fine medieval buildings such as orthodox monasteries, and a well known art gallery. You can see a list of places of interest here.
However, foreign tourism is not a big industry in Minsk and if you are going there you should learn a little Russian or Belarussian, or at least take a good dictionary and phrase book.