This is what I'm talking about.
As it has gone about 3 months without a response, I'll take a crack at it. If nothing but for the archives (which was how I found this question!).
The area you are referring to is called the Szekely Land and its origin dates back to the historical kingdom of Hungary. A map for reference:
The kingdom of Hungary existed with these borders (more-or-less - excepting the Turkish conquest when it was partitioned) from c. 900 - 1918.
The Pannonian Basin was invaded by the Magyar confederation (the nomadic ancestors of the Hungarians who fought on horseback) under the rule of Almos and his son and successor Arpad beginning in c. 900.
Originally pagan, they used the fertile grasslands of the region as a staging ground for their raiding operations, which they launched into the neighboring Holy Roman Empire, Italy, and Balkan Peninsula. This made them but one of many nomadic peoples to do this (along with the Huns, Avars, and Mongols).
After a dramatic defeat to Emperor Otto the Great at the Battle of Lechfeld, the Magyars embraced a sedentary lifestyle. They began to adopt the European feudal system and ultimately King Stephen (one of Arpad's descendants) accepted a crown from the Pope and began the process of making Hungary a Christian kingdom.
Now, getting back to your question. Part of this is difficult to answer as we don't have the greatest knowledge of the demographics of Hungary throughout its history. The Pannonian Basin has been home to many peoples over time - Celts, Romans, Huns, Avars, Slavs, Germanic peoples, Romanians, and Hungarians - all of these at different times inhabited the area. Often our sources for the inhabitants come from Roman or Greek writers who did not have direct knowledge of the area's population.
This makes developing a demographic history difficult; we are forced to speculate to what extent the latter waves of migrants intermarried with the existing populations, to what extent they constituted a ruling class or brought with them demographic change, how homogeneous or heterogeneous the area was, and so on.
For example there is one hypothesis that the kingdom of Hungary (excepting Croatia) was of a relatively homogeneous "Magyar" culture prior to the Turkish conquest, but as a result of the invasion much of the region was depopulated. Then, waves of Serbs, Germans, and Romanians were encouraged to settle into the area as a means of repopulating it beginning in c. 1600. This then (as proponents of the idea would argue) results in the ethnically diverse situation we find Hungary in in the later eras.
I myself feel the reality is that Hungary was always an ethnically diverse nation, with only a plurality being ethnic Magyar, but I digress.
In regard to Transylvania which you have posted an image of, we know that the kings of Hungary granted several charters for this area beginning around c. 1200 to two groups of people - the Szekelys and the Saxons. It is likely then, like now, the majority of the "land beyond the forest" was inhabited by Vlachs (Romanians) and the kings wanted to bring these settlers in to expand royal power there.
The Szekelys (who are the ones you see in green) have an unclear origin; their mythology says they are the descendants of the Huns but this is dismissed by scholars. The working theory is that they are simply a subgroup or a subtribe of the Magyars (they have been shown to be the same people genetically and linguistically) who relocated to Transylvania likely to fulfill their historic purpose there as "border guards." Their job was to represent the ethnic Hungarian majority at the boundaries of the kingdom and defend it against neighboring peoples (in history this would have been the peoples migrating in from the steppe - like the Pechenegs and Cumans).
The Saxons were German settlers brought into the area to facilitate economic development. Traditionally there were seven towns granted special charters by the king for German habitation; this is the origin of the German name for Transylvania, Siebenburgen - "Land of the Seven Cities."
We don't see much of a legacy of the German habitation in the area, but the Szekelys still make up the ethnic majority in several counties.
How this area ended up a part of Romania dates back to the end of World War I, when in the peace agreement the Entente powers decided to redraw boundaries in Europe based on ethnic self-determination, and reward the minor Entente powers (Serbia, Romania) with land. The Treaty of Trianon was specifically signed with Hungary, which (along with other changes) resulted in the Vlach-majority Transylvania being given to Romania.
So in summation this area of green is a legacy of the medieval Hungarian kingdom that you can see in modern Romania!
