Again means something that is repeated.(adverb)
A football team running a play one more time is an example of running a play again.
Again is defined as returning to a place.(adverb)
Going to the store and coming back home is an example of coming back again.
See again in Webster's New World College Dictionary
Origin: ME agen, ayein < OE ongegn, ongean < on-, up to, toward + gegn, direct: orig. separable prefix meaning “directly up to,” hence, “facing, opposite”
See again in American Heritage Dictionary 4
Origin: Middle English (influenced by Old Norse i gegn, again)
Origin: , from Old English ongeagn, against.
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