A "mini fare" is a sale fare, which can be between 10-60% off the normal fare. These sale fares also come with different fare rules, including the policies about changing or canceling your ticket.
For instance, with a mini fare you cannot change a ticket - with a normal or flexible fare, you can. Mini fares are also typically limited to a certain number of seats available for sale at a certain time, so you may not find the same sale fare available the next day or even later on the same day.
It is always important to read all fare rules before purchasing any ticket.