日本の学生の多くは、18歳になるとこれまでの環境と大きく変わります。
For most Japanese students, when they turn eighteen, the environment (they have lived in) up until now changes a lot
これまでの環境 means "the environment up until now". In XのY, X describes Y. The sentence should still make sense if you remove Xの. For example, removing これまでの gives: ...18歳になると環境と大きく変わります "... when they turn eighteen the environment changes a lot", but removing の環境 gives a meaningless sentence: ".. when they turn eighteen the up until now changes a lot".
I'm surprised you asked about これまでの環境. For me the more confusing part is 日本の学生の多く. I'm a little unsure here so some confirmation from a more experienced speaker would be useful. I think 日本の学生の多く and 多くの日本の学生 are both valid. 多くの日本の学生 Would mean "many Japanese students" and we can certainly remove 多くの and leave a valid sentence: "Japanese students, when they turn 18 ...". With 日本の学生の多く I think it better translates as "most Japanese students" and again I could remove 日本の学生の to get "Most, when they turn 18 ...", though there would have to be previous context for you to know who 'most' was referring to.
Finally, the と in これまでの環境と大きく変わります. The stripped down sentence would be 環境と変わります. This と is a particle marking a comparison. It is comparing これまでの環境 (the environment up until now) with an inferred new environment and saying that there is a change. Perhaps this post explains it better than I can.
Edit
Note that the translations offered above are rather loose. As discussed in the comments the subject of 変わります should be the environment of the student before they turn 18, but this is omitted from the sentence. To be clear, the phrase marked with と is the thing that is being compared against and not the thing that changes. The full structure should be XがYと変わります -- X changes compared to Y. But Xが (the previous environment) has been omitted. This makes the original sentence rather clunky.