In 1904 Iceland got home rule. Fourteen years later they went into a union with Denmark in which they only shared a common foreign policy, coast guard and head of state, which virtually gave Iceland independence.
Why was Denmark willing to do this? What is the context behind it?
Sæll :)
Iceland's battle for independence had been very long and very arduous. In 1871, Denmark forcibly induced a new code of law for Iceland called the Status law. Among many other things which Icelanders had not wished for, the Icelanders' right to vote on the Danish parliament was revoked. It dictated which matters Iceland was allowed to handle on their own, and which they were not.
Iceland's future parliament, Althing, was little more than an advisory committee when it came to subjects that mattered. It tried to ignore all other matters but the Status law and interpreted it so that the law was only a declaration on behalf Denmark, and was not actually a binding contract for Iceland. Denmark answered this by establishing a powerful office which was chosen by the king. This office oversaw matters which had previously been fully handled by Icelandic officials.
The Danish government conceded a little by granting the Althing rights to write their own laws, with the king's approval, in 1874. I'm not certain what you mean by home rule, but you're right that Iceland got its first Icelandic minister, as it was a position previously filled by Danish officials.
From 1874 to the first years of the 1900s, the battle revolved around the minister of Iceland.
In 1908, an important concession was made on behalf of Denmark. They planned on allowing Icelanders to reject (after 25 years) the Danish court, coast guard, Danish citizenship, and the Danish flag. Icelanders were not allowed to reject the office of the king, foreign affairs or military defenses. However, this concession was rejected on the Althing, because the independence-minded Icelandic officials wanted a mere personal relationship between Denmark and Iceland, but that was unacceptable for the Danish government.
We have arrived at the year in question; the year 1918. The battle had almost been won already before the discussions in 1918 even started, as the concessions made by Denmark in 1908 were pretty close to what Icelanders wanted. Not quite, though. The two poles differed in what they thought ought to be rejectable and what should not.
There were hefty debates in the beginning as the Danes wanted to hold on to the concessions made in 1908, but they finally agreed on that the contract in its entirety was to be rejectable, and Icelanders could in turn come to terms with a mutual citizenship and Danish foreign affairs taking care of Iceland's.
The rejectability meant that either country could, after 1940, demand revision of the laws. If a new contract wasn't made in three years, either parliament (the Danish one or the Althing) could, without consulting with the other, dictate that the contract was no longer valid.
With all this said, you can see that it wasn't a sudden shift of perspective that made the Danes make those huge concessions. It was simply the result of a painstaking independence battle on behalf of Iceland--reaching so far that, in 1918, the Danes declared that "they were open to discuss anything, so that the Icelanders weren't constantly finding something to argue about."
I hope this answered your question.
Source: From tyranny to democracy by Heimir Þorleifsson.