section 14.4 in pattern recognition and machine learning (free) says
Given a greedy strategy for growing the tree, there remains the issue of when to stop adding nodes. A simple approach would be to stop when the reduction in residual error falls below some threshold. However, it is found empirically that often none of the available splits produces a significant reduction in error, and yet after several more splits a substantial error reduction is found.
I am aware of the procedure how decision tree algorithm dividing training examples, I just want to know what does reduction exactly mean in machine learning?
As a commenter noted, this isn't really a technical usage. What they are saying is that, whenever we grow the tree another step, the error will get smaller. However as we start to overfit, the error will generally go down less than it did on earlier steps. So we set a threshold (say $0.1$) that says "if the error only goes down by $0.1$ or less, we stop growing the tree". That's what's meant by "we stop when the reduction in error falls below some threshold".