How does portion of a field get separated when charge is accelerated? I am a beginner and I was reading the book INTRODUCTION TO
ELECTRODYNAMICS by David J. Griffiths when I came across this line:
When a charge undergoes acceleration, a portion of the field “detaches” itself,
in a sense, and travels off at the speed of light, carrying with it energy, momentum, and angular momentum.
What does this mean? How does it take place?
 A: For a full answer you just need to keep reading the book.
Ultimately there is just one electromagnetic field filling the entire universe. It is continuous. No part of it is detached from any other part. However, when the field falls to zero in some spatial region, and then is non-zero somewhere else, then you could say that you have two separate regions of field, "detached" from one another.
In the case of an accelerating point charge, the field is the sum of two parts, one of which is very much like the field of a static charge and falls away as $1/r^2$, whereas the other part is like a spherical wave and its amplitude falls as $1/r$. So once you get far enough away this second contribution dominates, and one may speak of a piece of field which is much greater than the $1/r^2$ part of the field from the charge so it looks like a wave of non-zero field in the region where the static field of the charge is close to zero. In this sense it has become "detached". The wave keeps on propagating away from the charge.
Imagine the following situation, where the math is quite similar. Get a wide rubber membrane and attach it to a circular support, like a drum, but imagine a very wide drum. Push down on the membrane with your finger, somewhere far away from the distant circular support. You thus create a static depression in the membrane. Now wiggle your finger a little. Now there will be ripples on top of the static depression. They will propagate outwards, and the interesting thing is that you will be able to see them comfortably well beyond the region where the static depression is noticeable. (It works better in 3D but that is harder to visualize).
There is lots of lovely physics here. For example, the total energy and momentum of the propagating wave exactly balances the energy and momentum lost by the accelerating charge! It took a long time for physicists to work this out fully, but that is another story ....
