Denmark, Iceland and
Faroe Islands shared a more or less homogenous 'viking' culture in the Viking Age (800-~1050 CE), and Finland, while not strictly speaking a 'viking' country, did have a 'viking age' and a culture very close to its western neighbours, and at the close of Viking age was united into the Swedish kingdom.
Scandinavian culture today could be described as a potpourri of this "original" culture, medieval German influence, French influence in the centuries that followed, and several other smaller sources, not forgetting local development and national romantic inventiveness, of course.
A significant factor is also the fact that the Nordic countries never had an era of feodalism to speak of; personal freedom is highly valued here. The Nordics are rather heavy drinkers, the 'vodkabelt' goes right through Finland, Sweden and Norway; the Danes was more of a beer-drinking nation, but don't say no to a glass of akvavit either. In the last part af the 20th century vine get a big part of the former beer market.
Smorgasbords with pickled herrings and openfaced sandwiches with their layered toppings are no rare sight. Women are emancipated. Cities are clean and well-functioning enough to make a Swiss clocksmith feel at home. And so forth; myths and stereotypes about Scandinavia are many. Some of them are, of course, less true than others, but their very existense illustrates the fact that we do have quite a lot in common.
The English maxim of "my home is my castle" is usually not found in Denmark, where most families happily open their doors to friends and acquaintances, offering guests the best one has, thus creating that special Danish inclination for comfort called "hygge" - an all-embracing feeling of warmth and well-being, which freely extends, when the opportunity presents itself, to foreigners, who rarely will find it difficult to get into the mood.
A very common Nordic icebreaker - the weather! Too hot, too cold, too wet, too dry..
Swedish, Danish, Norwegian, Icelandic and Faroese are all Germanic languages developed from the Old Norse spoken in Viking age Scandinavia. A Swede, a Dane and a Norwegian can understand each other with varying degrees of difficulties, but none of them will fully undestand Icelandic or Faroese without studying the languages. But in the 21th century many younger people seem to miss this brotherhood-ear, and quite often just use English.
The Old East Norse dialect was spoken in the Danish settlements in Normandy. Old Norse was back in time also shared by England, Wales, Isle of Man, Vinland, the Volga and places in-between. Very fine map here about Old Norse and related languages in the 10th century.
Finnish is an entirely different case, it's a Finno-Ugric language related to Estonian and Hungarian. There is, however, a Swedish-speaking minority in Finland, which ties it linguistically to Scandinavia. Also, Finnish is related to Sami, the language spoken in Norway, Sweden and Finland by the Sami or Lapps, the aborigines of northern Scandinavia.
From the Viking age onwards, the Nordics have fought each other, formed unions with each other and ruled over each
other. Sweden ruled over Finland for over 600 years, Denmark ruled over southern Sweden also for over 600 years (or, alternatively, Sweden has ruled over northern Denmark for the past 300 years) and over Norway for nearly 500 years, while Norway ruled over Iceland for some 200 years and Denmark yet another 500 years..
..and the list goes on, but Finland hasn't ruled over anybody, and is very jealous because of that . Unavoidably, this has caused some antipathies, but it has also made the Nordic cultures more uniform.
The Germanic pagan religion has left it's marks on customs and festivals; celebrations with bonfires and maypoles mark the Finnish and Swedish midsummer, and the Nordic Christmas bears many similarities to the midwinter feast of the vikings, starting with the word for Christmas (sw. Jul, fin. Joulu) which comes from the Old Germanic word "hjul", meaning the wheel of the year.
Trolls and gnomes still inhabit Nordic households, although the once revered and feared mythical beings have been reduced to the lowly caste of smurfs and other soft toys.
The Nordic countries were converted to Catholicism in 10th to 12th centuries, but the Lutheran reformation embraced in all Nordic countries wiped out most of the Catholic customs and memories in the course of the 16th century.
Having become a stronghold of protestantism against Catholics in the south and Greek Orthodoxes in the east had some unifying effect on Scandinavia even though wars between the countries kept raging on; religion was, after all, the most important basis of ones identity well into the 18th century.
The Lutheran ideal was to require the common people to be able to read the Bible on their own, which had a enormous educating effect on the Nordic peoples. This, along with the protestant work ethics, had significant role in the forming of the Scandinavian societies, enabling their economic and cultural growth and the pioneering work that the Nordics have played in decreasing social inequality.
No doubt it also shaped the national character of each country to a similar direction. Before the 21th century a common complaint was.. "we're such joyless, grey and angst-ridden people" --> it's all the Lutheran Church's fault!
Norway, Sweden and northern Finland form the Scandinavian peninsula. Denmark is mostly a part of continental Europe, while Iceland and Faroe Islands is situated in the Atlantic Ocean.
Except for Iceland and Faroe Islands, the countries are situated close to each other, often sharing borders with one another, and have access to the Baltic Sea.
They do not really form a geographical unit, but this is rather irrelevant since seas and waterways have historically, instead of separating peoples, united them.
And we are, after all, talking about the best seafarers of ancient Europe. From childhood most of us still learn to use and connect living with the see, mostly in connection with weekends and vacations, and many have still today the sea as workplace.