Why not omit ‘this’ in the sentence
Why is John going over to the shop this early in the morning?
I cannot understand what the ‘this’ means in the sentence above.
this early means something like “now, which is very unusually early”.
Why is John going over to the shop early in the morning?
If you omitted this, the question could be asked at any time of day. The asker wants to know why John is going over to the shop early in the morning, which would most likely be tomorrow morning.
Why is John going over to the shop this early in the morning?
This question can only be asked at the time John is going or has recently gone over to the shop, which is early in the morning. Right now it is an unusually early time for John to be going over to the shop.
Present tense:
John normally goes to the shop at 8am. Right now, he is leaving to go to the shop and it is only 6:30am. "John, why are you going to the shop this early?"
Past tense:
John normally goes to the shop at 8am. Yesterday, he left to go to the shop and it was only 6:30am. "John, why did you go to the shop that early?"
Future tense:
John normally goes to the shop at 8am. Tomorrow, he is going to the shop at 6:30am. "John, why are you going to the shop that early?"
For more detail on using this/that to express proximity, see this article: https://english.stackexchange.com/questions/36527/at-this-time-vs-at-that-time