Mimesis refers to an imitation of nature, or the practice in writing of "showing" through direct representation instead of "telling."
Mimesis is primarily associated with Plato (Ion, The Republic) and Aristotle (Poetics) who contrasted this method of direct representation with its counterpart, diegesis (see definition). Aristotle, in particular, claimed that people are inherently "mimetic" beings, containing within a drive and an impulse to imitate and capture reality through art. Another way to think about mimesis in texts, specifically, is through dialogue. Mimesis is most readily understood when contrasted with its counterpart, diegesis; the Wikipedia "mimesis" entry provides an especially apt claim on the subject: "mimesis represents, diegesis reports; one embodies, the other narrates; one transforms, the other indicates; one knows only a continuous present, the other looks back on a past."
"'Is there a police station near?'
'Up in town. Why, what's wrong?'
'There's a body out on the reef.'
'Right out there--wedged between two rocks. A girl.'
'Say--' said the man. 'You get a bounty for finding a body. I forget how much.'
-John Steinbeck, Cannery Row
"Showing, enacting (as opposed to telling, recounting)" (Prince 52) -Gerald Prince, Dictionary of Narratology
"Direct presentation of words and actions of characters; often called 'dramatic'" (Martin 124) -Wallace Martin, Recent Theories of Narrative
"The imitation of action by performance" (Abbott 193) -H. Porter Abbott, The Cambridge Introduction to Narrative
Prince, Gerald. Dictionary of Narratology.
Rimmon-Kennan, Shlomith. Narrative Fiction.
Herman, Luc and Bart Vervaeck. Handbook of Narrative Analysis.