Alternative and related questions:
Can you describe a situation where you've been tactful?
Can you describe a situation where you're been diplomatic?
The meaning behind the question:
No hidden meanings here. Tact and diplomacy are invaluable life skills and the interviewer wants to assess your capacities in this respect.
Your answer:
Tact: Skill and sensitivity in dealing with others or with difficult issues.
Diplomacy: Skill and tact in dealing with people.
(Source: Oxford English dictionary)
As you can see, tact and diplomacy are inextricably linked. It's all about how well you deal with other people, particularly with respect to difficult people and difficult issues. It follows hot on the heels of the previous question.
While it's frequently important to be assertive, at other times you have to know when to bite your lip. Empathy is vital for effective relationships. There's a time and a place to assert yourself and a time and a place to be a little more mindful of what you say. Show the interviewer that you understand this important distinction.
Example:
Tact and diplomacy are all about skill and sensitivity in dealing with others, particularly when dealing with difficult people and tricky situations. I'm certainly capable of asserting myself when necessary but I'm equally capable of carefully controlling what I say if there's a risk of hurting someone else's feelings or causing some other negative and counter-productive reaction. It's a fine line one has to tread and it clearly requires a great deal of empathy. Understanding other people and empathissing with the way they think and feel is essential to effective relationships. It's also a question of context. You may find that you can say something to someone in private which it would be a very bad idea to say in the presence of others.
Word of warning:
If you're asked to describe a specific situation then clearly you must choose one which portrays you in a positive light without being undiplomatically critical of former bosses, colleagues, etc. It's a good idea to pick a situation involving a difficult client or customer, although, again, try to be tactful when describing them!