The allative case is a fancy way of saying "to something". It's like when you want to give something to someone and you say "I'm going to give this TO you". In grammar, that "to you" part is called the allative case.
Let's say you have a friend named Sarah who lives in a different town. If you want to send her a letter, you would use the allative case to say "I'm going to send this letter TO Sarah". The word "to" tells us that the allative case is being used.
In some languages, like Finnish and Hungarian, the allative case has special endings that are added to the end of a word to show that it's going to something. In Finnish, for example, if you want to say "I'm going to the store", you would say "Minä menen kauppaan", with "-aan" being the allative ending.
So basically, the allative case is a way of showing that something is going towards something else, like when you give a present to someone, or go to a different place. It's like a little arrow, pointing the way!