The way to explain what a montage is basically is a couple of clips that are put together of different dates and times of the character or an event progress in the short amount of time that is show to us or tell us a big story and tell it very fast.
the reason on why the filmmakers do this is for the people that are watching to see the progress grow and it give the people an understanding on what is going on in the short amount of time instead of just showing all of what has happen.
how i would used montage is start with the character struggling with something (like boxing) then show the character slowly improving then at the end show that the character has made the thing that he was working so hard for look easy for the character.
the purpose of the of the montage is to show all the people watching the progress on the event or the character.
to examples of montage in movie are “rocky” with his training to beat his opponent but struggle first but then began to improve because of his training and another montage is in the movie “up” when it show the marriage life of the two main character and show them in clips getting old together, over all there are many type of montage that can be happy and sad.