"To mark the occasion" can also mean to celebrate something. Examples: The couple had a huge party to mark the occasion of their tenth wedding anniversary. Joe had a recent promotion at work. His coworkers presented him with a gift to mark the occasion.

"Mark the occasion" means to make a note of whatever "occasion" (birthday party, family trip, etc) on your calendar, or just in your head. Basically just make a mental note of it, and remember that you are going to be at this occasion! If you have any more questions just message me :D