No. Until recently, it did give a person the right to sit in the House of Lords (the upper House of the British Parliament) but 'reforms' under Blair's Labor government removed that right. The members of the House of Lords are now nearly all 'Life Peers' chosen by the government for life, sometimes for good reasons, sometimes... well, let's not go there.
For example, William is now the Duke of Cambridge. What does that imply? Does William now have any control over Cambridge? Does he have a veto power on who becomes the next mayor of Cambridge?
No. There are a couple of titles in Britain that still convey some powers for historical reason, but only a few. Most are simply traditional honours.
Or is “Duke of Cambridge” nothing more than an empty honorary title?
It can't be called an honourary title, because that term actually has another meaning (ie, Generals Eisenhower, Patton, Bradley, etc, Admiral Nimitz, and quite a few other senior US officers before and since were all honourary Knights - Britain honoured them for their service as allies, but US law meant they could not, of course, bear foreign titles), but it is symbolic, rather than meaning anything concrete.
Thanks for the detailed reply to my question.