Meanwhile is most often used as an adverb and means "as this was happening."
For example - "I went to the store. Meanwhile, my daughter did the dishes."
This means that my daughter did the dishes at the same time that I went to the store.
Meantime is a noun that names the passage of time while something else is happening.
For example - "I went to the store. In the meantime, my daughter did the dishes."
It has the same meaning as the other sentence.
A common way to use "in the meantime" is when you have to wait for something to happen, but you want to do something else until then so that you are ready when the time comes.
For example - "We have to wait for Joe to arrive before we can start painting. In the meantime, let's get all the supplies out."