Hilary term is the second academic term of Oxford University's academic year. It runs from January to March. It is the term that begins on the first sunday after the feast day of St Hilary of Poiters, 14 January and all the other terms are dated from this day in the following way.
Michaelmas term - 13 Sundays before to 5 Sundays before the feast day of St Hilary Hilary term - 1 Sunday to 9 Sundays after the feast day of St Hilary Trinity term - 15 Sundays to 21 Sundays after the feast day of St Hilary
Michaelmas term
http://en.wikipedia.org/wiki/Michaelmas
Trinity term is the name of the third and final term of Oxford University's academic year. It runs from April to June. Examinations are usually held during seventh week of this term, and are usually followed by a tradition called trashing.