Have you ever had a friend ask for your opinion? Maybe she created some artwork or got a new hairstyle. Suppose you weren't impressed. If you found something honest but nice to say, then you demonstrated tactfulness. If you bluntly said that the artwork or hairstyle stunk like an old gym sock, then you showed a lack of tact.
Tactfulness is a character trait that keeps you from hurting someone's feelings. It's the act of being considerate and discreet when you talk. Another word for tactfulness is sensitivity. The opposite is tactlessness, callousness, or indiscretion.
Some people believe that being tactful must involve little white lies. For instance, if your best friend sings like a frog with a sore throat, you may not wish to say so and risk hurt feelings. You might think that exclaiming over your friend's "talent" is the kinder thing to do. However, honesty is important in any relationship. Even a little white lie may get you in trouble later. A tactful person would find something truthful but kind to say, such as "I like how enthusiastic you are when you sing" or "I've never heard it sung quite that way before; that was an interesting rendition."