Abarim Publications' online Biblical Greek Dictionary
The preposition μετα (meta) describes a presence in or motion toward the middle, within or among (hence words like metabolism, metaphor and metamorphosis). It often implies awareness of what the object (a person) is situated within (other people), and often comes close in meaning to the preposition συν (sun), meaning together or with. The difference between the two is that μετα (meta) emphasizes presence while συν (sun) emphasizes relation.
Sometimes μετα (meta) is used in a temporal sense: within six days, or after a while. In the vast array of compound words featuring μετα (meta) as prefix, it implies fellowship, proximity or a motion toward that. In compounds, it sometimes curiously expresses a degree of transition, and hence takes on the meaning of over, and even out of.