Meanwhile means while a particular thing is happening.
Brush the aubergines with oil, add salt and pepper, and bake till soft. Meanwhile,
heat the remaining oil in a heavy pan...
Kate turned to beckon Peter across from the car, but Bill waved him back, meanwhile pushing Kate inside.
Meanwhile means in the period of time between two events.
You needn't worry; I'll be ready to greet them. Meanwhile I'm off to discuss the Fowler's party with Felix.
You use meanwhile to introduce a different aspect of a particular situation,
especially one that is completely opposite to the one previously mentioned.
He had always found his wife's mother a bit annoying.
The mother-daughter relationship, meanwhile, was close.
If something happens while something else is happening,
the two things are happening at the same time.
Racing was halted for an hour while the track was repaired...
Her parents could help with child care while she works.
If something happens while something else happens, the first thing happens
at some point during the time that the second thing is happening.
The two ministers have yet to meet, but may do so while in New York...
Never apply water to a burn from an electric shock
while the casualty is still in contact with the electric current.
You use while at the beginning of a clause to introduce information which
contrasts with information in the main clause.
The first two services are free, while the third costs £35.00. = whereas
You use while, before making a statement, in order to introduce information
that partly conflicts with your statement.
While the numbers of such developments are relatively small, the potential market is large...
While the news, so far, has been good, there may be days ahead when it is bad. = although