I understand that the degree of a node is the number of children it has.
However, how do we define the degree of a tree?
For a rooted tree you might define it as the degree of the root. In some scenarios saying it is the maximum degree of any node in the tree might make sense. But without context it is hard to say what the right definition is. It depends on how you want to use it and what is significant about the "degree" of a tree. If you have a concrete example in mind, or a piece of text that you find puzzling, please update the question.