A living trust is a legal document similar to a will but the difference between the two is that it is quicker for a living trust to be implemented after the death of someone because it doesn't need to be probated like a common will. So, the procedure is faster.
The children in the example will benefit because they will be given what the living trust determines they should get immediately after the death of their parents. Also, if their parents have assigned a legal guardian for them in the living trust, they will have someone who will take care of them immediately.