"Conditional" -- at least in my Descriptive English Grammar course -- is one possible modality of verbs in English. The four modalities are indicative, conditional, imperative, and interrogative. The conditional modality is used for a number of purposes. Perhaps the three most common purposes are:
1. To express future meaning, using the modal auxiliary "will." E.g. I will call you tomorrow.
2. To be polite, using any number of modal auxiliaries, mostly "could" or "would." E.g. Could you give me a call tomorrow? or Would you be so kind as to give me a call tomorrow?
3. To express statements that are only probability or are even contrary to reality. E.g. I would give you a call if I had the time.
To write an extensive essay, I would recommend that you focus on these uses -- and on other uses -- of the conditional in English. Give at least one solid, preferably real example for each use. You may want to use an internet search engine and put quotation marks around the terms (such as "I would" and "I could") to see what sorts of real uses are out there.
You may also want to discuss less standard (but still very real) uses, such as using "have to" or "ought to" instead of "must" and "should" or even using double modal auxiliaries such as "might could" and "might ought to."
Of course, you may have other "conditionals" in mind, such as "if" phrases (e.g. If I were king, I would....). Be sure to write the paper on the precise topic that the instructor wants and, if possible, ask the instructor directly if you have any questions or would like to see some examples.