Step 1: Recall the frequency list of orbital neoplasms. The leading benign orbital tumor of adult life is the cavernous hemangioma.
Step 2: A cavernous hemangioma is built from large, blood-filled vascular channels separated by fibrous septa, so its parent tissue is vascular endothelium, meaning it springs from blood vessels.
Step 3: Clinically it produces gradual, unilateral, painless forward displacement of the eye, and it is the typical intraconal mass seen on imaging.
Step 4: Eliminating the other choices: neural tumors (glioma, meningioma), myogenic tumors, and lymphoid masses all rank below vascular tumors in overall incidence, so none of them is the answer.
\[\boxed{\text{Blood vessels (cavernous hemangioma)}}\]