Based on the current consensus of dictionary definitions and my own ongoing literary experiences, I would feel comfortable defining an essay as an analytical, interpretative, or occassionally informal literary composition, usually of a concise length though sometimes longer, which engages in a given topic often for the purpose of advancing an author's thesis or point of view to her or his audience.
Essays can be formal, informal, satirical, even poetic.
Literature's evolution has enabled the essay to accommodate the demands of the ages and assume the broadest or narrowest of subjects. Despite its past and present success, the essay is still one of the most underestimated, under-celebrated modes of human expression. Plainly put, our appreciation of the essay is not, this author believes, where it could or should be. The essay sprouted from the simple needs of advancing ideas. Like any plant it grew taller and many branches, and the essay is a tree today in the forest of literature, one with strong, deep roots in the history of human expression.