A propempticon is a type of poem written in classical times with the purpose of sending a friend on a good journey. Essentially, it would be sent to wish a friend a speedy arrival (since travel was by no means safe or easy in classical times), as well as to provide him with a source of amusement during the journey that could also serve as a memento of its composer.
One of the most famous propempticons is the 3rd poem of book 1 from Horace’s Odes, which he wrote for another famous Roman poet, Virgil. Other famous propempticons not only seek to entertain their recipients, but some attempt to warn them of the dangers of travel, or to dissuade a loved one from making a perilous journey, et cetera. Since this form of poetry was largely practised in antiquity, most poems in this style are written in some form of Ancient Greek or in Latin.
The term propempticon is very difficult to look up (many dictionaries do not carry it as an entry), and so etymological information is hard to come by. The term is well known by people who study the classics, however - especially those who study classical poetry. While I know very little Ancient Greek, I am certain that the word comes from the Greek verb “pempo” meaning “to send.” (My source for this is Chapter 4 of the Third edition of Alpha to Omega: A Beginning Course in Classical Greek, by Anne H. Groton) the prefix is most probably from the Latin prefix “pro” meaning “on behalf of, for, forward,” among other things; and so you can see how the word would come to signify something that is used to send someone off on a trip.
Note: This type of hybrid etymology, consisting of both Greek and Latin elements, is not unusual: television and automobile are both examples of common words which consist of both Latin and Greek elements.