This is the 210th most frequent Dutch word.
bezig
Busy; occupied.
Here, 'bezig' indicates that the children are occupied with the task of doing their homework.
De kinderen zijn bezig met hun huiswerk.
The children are busy with their homework.
In this sentence, 'bezig' emphasizes the ongoing nature of the preparations for the party.
We zijn al bezig om de voorbereidingen te treffen voor het feest.
We are already in the process of making preparations for the party.
The word 'bezig' signals that the speaker is currently engaged in the activity of writing a book.