Do you want to know the "meaning" of graph embeddings? I recently wrote a Medium article that discusses this topic from different points of view, including:
Euclidean vs non-Euclidean Geometry
Positional vs Structural Embeddings
Transductive vs Inductive Learning
Unsupervised vs Supervised Tasks
https://towardsdatascience.com/graph-representation-learning-network-embeddings-d1162625c52b
Enjoy!