Many travelers and locals alike hail Japan's shinkansen network as an efficient and comfortable way to get from A to B. If you've traveled on the shinkansen before, you may have seen certain carriages labeled with a sign saying "green car" and wondered what that meant.
The green car on shinkansen is a little more expensive than the standard cars, but they offer more spacious seats, better legroom, and they're in a 2 + 2 configuration rather than a 3 + 2 like most regular cars provide. You could liken green cars to the business class of the shinkansen, with the regular cars more aligned with economy class.
I've traveled in the green car a couple of times when my children were younger, and found it very useful during that season of life. It was nice having the additional space for all the extra bits and pieces you have to carry with you as a parent, and the cars were typically empty or only shared with a few other passengers. If you've got little ones who still nap, it's great in that respect!
Something to keep in mind with the green car is that reservations are required, so you would need to visit a JR ticket office to get that sorted. You don't have the same flexibility as you do with an unreserved ticket, where you can keep your travel plans a bit more on the fly.
I don't know that I would necessarily use the green car now that my children are a little bit older – I feel like the regular cars offer enough space and are typically very quiet anyway. However, if you have a little extra cash to spend and you value the prospect of an ultra quiet ride, larger seats, and extra leg room, I'd definitely recommend them. Happy traveling!