Suppose today is Wednesday and someone told me to schedule the meeting on the coming Friday. Which Friday would that be?
Jitendra, welcome to EL&U.
“This coming Friday” is “The Friday which is imminent”. That is if today is Wednesday the 9th “This coming Friday” is Friday the 11th. This is to distinguish it from “Next Friday” which is often taken to be the Friday of the next week.
“This coming…” can be used with any day of the week and can be used to refer to a day in the next week. For instance if today is Wednesday the 9th you could say “This coming Monday” to mean Monday 14th although there is some overlap there and Monday could also be called “Next Monday” because Monday is so far away from Wednesday and is in the next week. As I said “This coming…” is used sometimes because “Next…” can be interpreted in more than one way.
“This coming…” used to be rather more common than it is now as people now tend to just use the name of the day to refer to the imminent one. If today is Wednesday 9th most people will now say “Can you arrange a meeting for Friday please?” When they mean Friday 11th, they would tend to use “…this coming Friday” only if the other person asked which Friday. Indeed “This coming Friday” would most frequently used in this way:
Person A: “Arrange a meeting for next Friday please”
Person B: “This coming Friday or Friday next week?”
Person A: “This coming Friday”
However if today is Thursday the 10th it would be unusual and confusing for anyone to say “This coming Friday” because that would be better described as “Tomorrow” and Friday the 18th would be “Next Friday”.