The DEGREE of a vertex is a number that specifies how many edges touch that particular vertex.
In addition, if a graph is directed, then each vertex has an INDEGREE and an OUTDEGREE. The INDEGREE of a vertex specifies how many edges have their head in that vertex. This can also be thought of as how many edges point to that vertex.
The OUTDEGREE of a vertex specifies how many edges have their tail in that particular vertex. Likewise, this can be thought of as how many edges point away from the vertex.
In the example, 7 edges touch Vertex A, so Vertex A has DEGREE 7. Vertex A has an INDEGREE of 3 and an OUTDEGREE of 4.
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