completed, have done 下了
some, a series of, 一番
difficult struggle 苦功
Together it's a statement that shows acknowledgement of someone's effort.
It is a comment and at the same time a praise when used appropriately.
A boss may look at some employee's work and say approvingly:
"(Very well,) I can see you really have put a lot of effort into this project."
Chinese people believe in hard work. To them, pain and constant struggle are necessarily an integral part of someone's success and survival. The ability to endure that hardship is considered as a virtue. Ex. 她很能吃苦
Therefore you should expect a smile when you say this to Jane:
"Jane, I noticed your English has improved a lot! 你 (真的/的确) 下了一番苦功."
Another example can be:
"Jane, I like this painting of yours. 你 (真的/的确) 下了一番苦功."
(Your painting skills really have improved a lot.)
But try not to use this expression with your boss. Modern Chinese society is still quite hierarchical.
Commenting is what superiors do to their subordinates, usually not the other way around.
However, It is totally appropriate to use it with your friends or people whose 辈分 is lower than you.