Tactful is the adjective for tact. It describes someone who is careful with other people's feelings when saying something difficult, or it describes the words and acts themselves — a tactful reply, a tactful question, a tactful silence.

So it works two ways. Applied to a person, it says this is how they generally are: 'she's very tactful' means you can trust her with an awkward conversation. Applied to a thing, it praises one particular choice: 'that was a tactful way of putting it' means the words were well chosen for this moment, whoever chose them.

A useful pattern to hold on to is 'it would be more tactful to…', which is how English quietly suggests a better way of doing something without criticising the first way outright. You will also meet 'a tactful way of saying', which often introduces a gentle euphemism — 'he's between jobs' is a tactful way of saying he is unemployed.

Watch the shape of the opposite, since students get it wrong constantly. The opposite is tactless, not untactful. A tactless remark is one that hits a sore spot because the speaker did not stop to think — clumsy rather than cruel. That distinction is exactly why English keeps the word: it lets you criticise the thoughtlessness without accusing anyone of unkindness.

Register is neutral, leaning slightly formal. It sits comfortably in ordinary conversation, and it is a common word in job descriptions and in advice about how to deal with people.