Abarim Publications' online Biblical Greek Dictionary
The preposition επι (epi) means on or upon. It survives in English in words such as epilogue (upon, or after the main story), epidermis (upper skin) and epicenter (the point on the earth's surface directly above an earthquake).
Our preposition is used in a great variety of ways, some implying rest (being physically located upon or logically completing a statement) and others implying motion (moving onto a location or towards a situation or understanding). It many provoke the genitive, dative and accusative cases, depending on context.
Our particle may reflect an overbearing authority or power, suggestive advice or motivational encouragement. It may even serve to indicate repetition (over-and-over), or as intensifier (above-and-beyond), like our prefixes "extra-" (extraordinary) or "super-" (supersonic).