In what area was Denmark more superior to those countries, so that it dominated them, such as military, trade, dynastic matters, political culture? How strong was the leadership of Denmark, and was it formal to the point that they were able to lead the country into wars, or enhance development, etc.? How long did this last?
The reason goes back to Queen Margrethe I of Denmark. (She is to the current queen, Margrethe II, what Elizabeth I of England was to Elizabeth II).
Margrethe was the Queen Consort of King Haakon of Norway-Sweden with whom she had a son, Olaf. She was also the daughter of King Valdemar of Denmark. The succession plan was to have the son take over both Norway and Denmark. But then her father died, her husband died, and her son died. So even though she was a woman, she was the last of the royal families of Norway and Denmark, and the nobles of those two countries chose her to be the Queen Regnant (a reigning queen).
The Swedes were not so accommodating. They had earlier elected Albrecht of Mecklenberg, a German prince, and a cousin of Haakon, as their new king. But the more logical contender was the newly crowned queen of Denmark-Norway. The two went to war, and Margrethe I won, thereby uniting Denmark, Norway, and Sweden into a so-called "personal union," the so-called Kalmar Union of 1397. Subsequent Danish monarchs maintained this arrangement until 1523, when the Swedes rebelled, and became an independent country under Gustav Vasa. Norway remained united with more-populous Denmark until that country chose the wrong side in the Napoleonic wars, and Norway was taken from her and given to Sweden, who had been a part of the anti-Bonaparte coalition.
Tom Au's answer above is mostly correct with regards to Norway; Albrecht actually had a formally stronger claim to the Norwegian throne, but was set aside since Margrete was so effective.
As for Sweden, Albrecht had been king there since 1364, and Margrete only really came to power in Norway and Denmark in her own name in 1387/1388 (she had been regent for several years then). At that point, the Swedish magnates had been able to reduce Albrecht's power greatly, but when it looked like he would regain it in 1386 when Bo Jonsson (Grip) (Sweden's most powerful non-royal person ever) died, they allied with Margrete. Exactly who fought on which side in the following war is not clear, but the end result is: Margrete won, and proved a much stronger regent than Albrecht ever was.
As for power, it should be noted that while Denmark-Norway was usually much stronger than Sweden during the 15th and 16th centuries, during the years before the Kalmar union, things were not always so. In the early 14th century, Magnus Eriksson inherited the Norwegian throne and was elected king of Sweden (this was mostly a formality at this point), he was also able to exploit Danish weakness and bought Scania. It was at that point in no way clear that Denmark would eventually end up the stronger power and stay so for over 200 years.
That it was can partly be ascribed to the Sound dues, which generated a steady, large revenue and gave the Danish king political independence from the privy council and diet. Denmark also had closer ties to Europe in general, meaning stronger diplomacy and easier access to mercenaries.
According to Wikipedia's article on the Kalmar Union, it was a personal union, and Norway, Sweden and Denmark remained separate kingdoms that happened to have the same king. Since the king usually resided in Denmark and had mostly Danish advisors it seemed to some Norwegians and Swedes, then and later, that their countries were being dominated by Denmark.
Unless someone can find an official text of the Kalmar Union documents that says that Norway and Sweden were now vassals of Denmark, the original question must be considered technically inaccurate. It would have been fun, though, to see a king acting as king of Sweden do homage to himself acting as king of Denmark!