Refers to the tree itself, not the blossoms. Common in everyday contexts.
公園に大きな桜の木があります。
There is a big cherry tree in the park.
桜の木の下でお花見をしましょう。
Let's have a cherry blossom viewing party under the cherry tree.
Compound of 桜 (さくら, 'cherry') + の (possessive particle) + 木 (き, 'tree').