Africans clearly stand out as the most willing to move from home, followed by Middle Easterners. Asians, meanwhile, seem most content where they are. Americans just slightly edge out Europeans as happier with their homes. Because the data is aggregated into regions, we shouldn't read draw too many conclusions from the map. For example, it's hard to imagine that the French are more willing to emigrate than the Afghans.
The second map, however, does break the data down into countries, revealing both some predictable and unexpected results. Predictably, as Andrew Sullivan points out, the United States is the most popular destination amongst the would-be emigrants. Approximately one quarter of the respondents, around 165 million people, chose the U.S. as their new home. Other popular countries included Canada, the U.K, France and Spain.
But surprisingly, even though 23% of Middle Easterners want to move elsewhere, Saudi Arabia was one of the most popular destination choices for emigrants, with 30 million people naming the desert Kingdom. In fact, if everyone actually moved to where they desired, Saudi Arabia's population would increase by 180%. Only Singapore would experience a larger percentage increase.
So, why do so many people want to move to a country that its own citizens want to leave? Without more exact data, it's hard to say for sure, but I'd bet the major factor is Islam. The Saudi interpretation of Islam, called Salafism, follows an extremely strict reading of the Qur'an. As such, it's largely a love it or hate it movement, with passionate followers and vehement detractors alike.
The Muslims who adhere to Salafism would understandably want to live in a country like Saudi Arabia. But I'd also imagine many Muslims around the world would willingly abide by such a strict interpretation of Islam, even if they personally do not subscribe to all of its tenants, in order to live near the birthplace of the Prophet Mohammed and the revelation of Islam. But at the same time, many Saudis find the conservative culture of their country constricting. In fact, Saudis are notorious for traveling to more liberal countries, like Egypt and Lebanon, in order to, putting it nicely, enjoy themselves and let loose.
In fact, you may have noticed that Egypt is another popular destination, likely for that very reason. As both a Muslim-majority and (relatively) socially liberal country, Egypt offers a good compromise for Muslims who are seeking a more open atmosphere that still maintains a level of cultural and religious familiarity. As such, I'd guess many Saudis would prefer Egypt over the United States, but that's just a hunch.
In short, we likely have a case of the grass is greener on the other side. Many Muslims want to live in a more conservative society like Saudi Arabia, while some Saudis wouldn't mind a little more freedom.
*As a side note, the Gallup poll only included Arab nationals and expatriates while surveying the Gulf countries like Saudi Arabia. In other words, the huge numbers of migrant workers (usually from South Asia) that work throughout the Gulf Arab countires were ignored. This brings up another motivation to move to Saudi Arabia - finding employment.