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"ordered by priority and by a key value" → it's unclear whether these are dimensions or additional properties of points, maybe ", one dimension corresponding to priority and the other to a key for the point"?
The operations supported should be described already in the lead, like "A query returns all points with keys in a given range [min_key, max_key] and priority below a given threshold max_priority.". This also makes it clear how keys are a dimension, with a linear order. The Description section can then focus on how it is implemented (how it stores those points).
Does the structure not support any modifying operations? If yes, then this should be mentioned in the lead, since "extension of priority queue" suggests otherwise.
"each nodes represent a point" → "each node represents exactly one point"?
"the lowest priority" → add "among nodes in its subtree"?
