So
first if im not wrong the mini-event are that provide influnce in different lands if so then!!
there are pleanty of different mini-events
they usually happen very often and some better ones not that often
the benefits are depended on the event you are doing some have very valuable stuff you can get from them!
so basicaly in these event you must do things like killing something or gather stuff in maps and etc
by doing that you gain influence,you may ask what is influnce
well by doing event you gain it and there are usually 3-4 tiers of items you get each need more influence they are one time deal when you get item you cant get it again!!! and on other cases you can do them all the time
but with that influnce you can as well unlock new pets that you can buy depended on which place influnce you have you can find that out in event section
and usually the last item is actualy something good potion that give stats for hour or even valuable gnome coins
And there are ones that you can do all the time they happen for example The Sorcerer's Revenge in that event there spawn 50 particles and you have to manage to gather 5 if you do so you get chaos particles which are very valuable to have or chaos breakthrough where you can kill strong bosses for chaos reputation
And last thing i wanted to mention that if you like to gather achievments than in some event in last stage you can kill bosses that give you them as well
if this what i just described actualy are not mini-event sorry