This question inspired the following: I should verify whether the prefix really means something. I quoted the French version of Wiktionary because the English version does not state the Latin etymons (only the PIE etymons).
The prefix op- originated ob- (e.g. obsto from *opsto), and is visible in operio (< *op-u̯eri̯ō) and oportet.
The verb derives from PIE *su̯er-, which means "to close, cover" or "to guard, save".
Given that aperio (< *ap-u̯eri̯ō), which means "to open", is formed with the prefix ap-, "from, out" (ancient Greek ἀπό), and at the opposite op- means at, by, around, round about, all around (ancient Greek ἐπί), in the case of operio the prefix could denote that the object is completely closed or enclosed.
For further references see the digital edition of the Indo-European Etymological Dictionary of Pokorny-Lubotsky (use the "find" function of the browser and search "aperi" or "operi").