On most routes, the airlines are aware that they can charge higher fares at certain times of the year. We have seen that H indicates High Season (also known as Peak Season) and that L indicates Low Season (or Basic Season).
In Rule 2745 for the Apex fare from London, UK to Bogota, Colombia, we are given the seasons: Low Season - 15 Jan-14 Jun and 16 Sep-12 Dec, with High Season - 15 Jun-15 Sep and 13 Dec-14 Jan.

The seasons are not equal in length; the High Season periods reflect the times that more travelers want to fly between London and Bogota. The two high seasons cover the one month Christmas & New Year period and the period between June and September.
It is not just religious holidays and weather that will affect seasonal fares. Local events and international conferences can affect the fares too. Look at these seasonal fares for London, UK to Seoul, Korea:

Seasonal Fares apply on many cheaper fares, not just Apex, so look out for the letters H and L in other fares.
On some routes, airlines split their fares into more than the two high and low seasons. Looking for more flexibility, they have a season that comes between the two, and its call the "Shoulder Season".
The Shoulder Season is usually shown by the letter K (or the letter J, or O, if there are additional "Shoulder Seasons").
Below are the seasonal Apex fares for London, UK to Lusaka in Zambia:
High Season Apex = YHAP
Shoulder Season = YKAP
Low Season = YLAP
High/Peak = H 
Shoulder = K or J or O 
Low/Basic = L 