It means they (all the citizens) began a migration into / to a colony. Here is another example, ボストンへの旅をしたい。Bosuton e no tabi wo shitai. = I want to take a trip to Boston. "Boston e no tabi" = "a trip to boston". Of course, you could always say ボストンに旅したい。too. :"Boston e no" is acting and adjective (although in English we would call it a prepositional phrase) here though. That is, it modifies the noun that comes after it. You can see this in Japanese advertisements with the word から (kara) as well. For instance, アメリカからのパソコン (Amerika kara no pasukon) which means "computers from America." Hope that helps. :)

への= into this case the citizen　begin(start ) to escape(move) into colony へshows drection の refer prevous noun to in one (english into ) The citizen move to one which is colony become same mean but this case easy to understand english preposition " INTO "