They are basically the same. It's just that the word "single" breaks each day apart and puts an emphasis on the fact that each day is separate. It gives the feeling, "time after time after time" or "again and again and again." Whereas when you say "every day" the days seem vague and/or connected, as though there is no separation/specific time. It is almost like the difference between saying, "I go to the gym Monday through Thursday!" vs saying "I go to the gym Monday, Tuesday, Wednesday and Thursday!" Even though it is likely that the listener knows what days are between Monday and Thursday, if the speaker doesn't list each of the days, the impact isn't as strong and there isn't as great of an emphasis as in the second sentence that lists out each of the days separately. Also, in normal speech if someone says that they study every night, it is possible that they have missed a night or two (as in something prevented them from studying for a night). However, if someone says, "I study every single night." They are saying that they have never missed a night of studying. Keep up the good work! :)

they almost have the same meaning, but "i study English every single night" is more precise, it means you never ever miss a night without studying English.

i think "every single night" is more like to emphasize every night.

Yes, but by adding the word 'single' it adds emphasis. It's a way of showing how diligent they are.

I study English every single night强调了自己的学习真的是really very very hard