If you give input one by one to the algorithm and each input produces some partial solution with available input data. Then that type of algorithm is known as an online algorithm.
Here in insertion sort, we give input one by one and place each one at right order with comparison from already traces element. We need not the whole array simultaneous to operate algorithm. so it is online algorithm.
Let A[] = {23,1,4,2,7}
step:
1. A[] = {23,1,4,2,7} ( only take 23 in consideration)
2. A[] = {1,23,4,2,7} (only take 23,1 in consideration)
........................ and so on.
While in merge sort, it needs the whole array then algorithm start operation. so it is offline.
I hope you get little bit idea about this !!
Plz, comment if you have still doubt !!