To elaborate a bit on what /u/TheBaris said: Turkey was in a weird position. The Ottoman Empire was a world power during its heyday and when the empire collapsed, it collapsed hard. In the chaos that followed, and the ill-advised attempts to partition the old Ottoman heartlands, the Turks found themselves fighting half their neighbors: Greeks in the west, French in the south, Armenians in the east, and various skirmishes with the Brits. Constantinople, the Ottoman capital since Mehmed II captured in 1453, was occupied. It was pretty much chaos. And Turkey was somewhat fortunate that the Russians were too busy fighting their own civil war to meddle in it.
Turkey eventually won, obviously. But the important thing isn't the battles or the casualty figures: it's the fact that Turkey was fighting the Entente. The men who came to the forefront of Turkish politics in this period -- Ataturk, Karabekir, Cebesoy, Inonu -- were fighters. Many of them fought in the Balkan Wars, most of them fought in WWI (Yazici, who would go on to command in Korea, fought at Gallipoli), and many of the men who would go on to hold high posts in Turkey (President, Prime Minister, Speaker) served some military role.
And then, while Turkey is still trying to find its place in the world (especially after the chaos that was WWII), it holds open elections and for the first time ever the government is dominated by men who didn't fight in one war or another. Bayar was elected in 1950 and the closest thing he had to military experience was as a young political radical (he would remain in office until the 1960 coup). His Prime Minister (who shared his long tenure), Menderes, similarly had no military experience. Koraltan, Speaker of the National Assembly over the same period, was in the same boat. As you can probably imagine, shifting from a government that was led primarily by former military officers or the politicians who worked with them to a government comprised almost exclusively of men who had never seen combat represented quite a shift in Turkish politics.
While all of this was happening on the domestic front, Turkish foreign policy was changing, too. Early in the republics history, it had committed to a policy of neutrality: it wanted no part of any alliances. Turkey and (most of) the great powers sat down and figured out what to do with the Bosporus and Dardanelles, leading to the Montreux Convention, which imposed all sorts of military restrictions on transiting those waters. Everything seemed all hunky-dory and then WWII happened. When the dust settled and the Soviets were triumphant, they suddenly had an enormous military advantage over Turkey. In 1945, the treaty of friendship between the two countries expired and was not renewed. In 1946, the Soviets sent two letters suggesting Turkey agree to "alter" the Montreux Convention by making the Soviets a guarantor of the treaty (which, in diplomacy-speak, means a permanent Soviet military presence in the area) and, while they were at it, the Soviets they wanted land, too. You can read a bit more about it here, which the relevant parts being around page 44 on (in the pdf reader; the pdf pages say it's page 27).
In the face of Soviet demands, the Turks really three options: capitulate and effectively become a satellite state, stand alone and risk invasion, or go to America. So the Turks went to America. As it happened, America was in the process of forming NATO, which would come into existence in 1949. To America, Turkey wanting in was a wonderful boon. Control over the straits, even if through an ally, was effectively a lever against the Soviets.
As an aside, it's probably worth noting that Turkey also hosted nuclear-tipped missiles from 1959 until 1963. If those dates seem odd to anyone, they may be interested in knowing that the Cuban Missile Crisis was in 1962. If that seems an odd coincidence, it's because it wasn't. The Soviets pulled their missiles out of Cuba because America agreed to pull their missiles out of Turkey, not because they were intimidated. It makes you wonder if the Soviets sent missiles to Cuba solely to get them out of Turkey. But I digress.
So when the Korean War broke out, Turkey had an opportunity: by sending troops there, it could achieve two objectives: it gave Turkey the opportunity to prove its commitment to America (and thus effectively guaranteeing NATO membership) and simultaneously align itself very publicly against the Soviets. It effectively sent a message that Turkey wasn't going to be bullied into accepting an unfair treaty by the Soviets and that, if the Soviets forced the issue, that Turkey would have friends that would help them. It would take until 1952 to finalize, but Turkey was effectively under NATO's aegis from 1950 on. 15,000 men sent to Korea was a small price to pay for that security.
Edit: gold? wat? :D
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I actually came into the sub to ask a related question, so I hope I can piggyback here: In this /r/HistoryPorn thread, one user asserts that "the Turks fought like mother fuckers", while another retorts that "the only useful thing they did was capture retreating ROK infantry" in the belief that they were North Korean.
The Wikipedia page on the Turkish brigade in Korea suggests that there is controversy over the performance of the Turks in Korea, with some claiming that they were under-trained and under-equipped, commanded by a Gallipoli veteran and only got the positive attention they did because their moustachioed soldiers looked the part of the seasoned warrior; others point to the Presidential Unit Citation and various contemporary accounts of their bravery and key role in certain actions.
So the question (which I apologise for approaching in such a roundabout way) is, what's the straight dope on the Turkish Brigade? A useful military force or a propaganda coup to remind everyone that it was a UN not just a US action?
Did the US augment the pay rate for these troops - bringing it up (I am assuming) to the same level as US troops. This could add up to a significant economic influx for Turkey as well as for other countries sending troops. The US dollar was king back then...
I don't have anything to add on the historical angle, but I can say that anecdotally, Turks still appear quite proud of their contribution to the Korean War. Living in Turkey, most of the time Korea comes up, some Turk will mention that the two countries are great friends because of these soldiers who fought in the Korean War. I don't think that Koreans have the same awareness, however, since to them it was primarily American assistance.
