meaning of 'on which'

I have searched in Google, dictionary and StackExchange and I couldn't understand. I want to know what is the meaning of 'on which'.

We call one of those sets the training set, on which we learn some properties; we call the other set the testing set, on which we test the learned properties.

Solution 1:

"on which" is an example of a construct where we reverse the order of subject and object around a preposition. The "on" can be any preposition, and "which" simply indicates that the preceding noun is the object of the preposition.

So

We learn some properties on this training set.

becomes

This is the training set on which we learn some properties.

Similarly

I bought some books at this shop

becomes

This is the shop at which I bought some books

and

I placed the food in that box

becomes

That is the box in which I placed the food.