This popular Latin phrase has been popularized in books, movies, and other media, but the original source of this phrase is ancient; It is from Horace’s (65-8 BC) Odes, a collection of his poems. The original line reads:
Carpe diem quam minimum credula postero. (seize the day and place no trust in tomorrow.)
From a student’s perspective, “Carpe diem" is a simple construction consisting of a verb in the imperative mood and a noun in the accusative case. “Carpe" is from the third conjugation verb “carpo" (carpere, carpsi, carptum) meaning to “pluck" or “divide." However, Horace’s use of the word, given the complete sentence above, was metaphorically intended to imply enjoyment or fulfillment. Hence, the word is often translated as “seize" to avoid confusion had a literal translation been used instead. Certainly “pluck the day" makes no literal sense in English.
Recall that third conjugation verbs form the present imperative simply by taking the present stem of the verb. In this case, the stem of the verb “carpo" is “carpe." To pluralize this phrase, recall that the plural imperative is formed by dropping the –e and adding –ite. In this case, we would have “carpite." (As a technical note, it is not that the –e is dropped as it is that the –e changes to an –i– with the addition of the –te to indicate that the command is intended for two or more people).
“Diem" is simply the accusative singular of “dies" meaning “day." It is in the accusative case because it is acting as a direct object of the action of the sentence; it is indicating what the listener or reader should seize. Recall that since the imperative mood indicates a command, it is always considered to be in the second person. There are no first or third person imperative mood forms because commands are given directly to the listener or reader. What “carpe diem" is really saying is:
Hey, you (singular)! Seize the day!
As a side note, the word “carpo" meaning to pluck or divide is the derivative of the word “carpal" in “carpal tunnel." The carpal tunnel is a passageway through which nerves of the hand pass. It is here that we see how the literal meaning of “carpo", to divide, also finds its way into English.