Someone who's matter-of-fact is straightforward and unemotional. Your matter-of-fact friend won't get upset when her dog runs away — she'll call him calmly until he returns.
Matter-of-fact things aren't fancy or stylish; they just tell it like it is. A matter-of-fact letter to the editor is practical and factual, and a kid's matter-of-fact apology for breaking his neighbor's window will take responsibility and offer a sincere "I'm sorry." A matter-of-fact news report doesn't sensationalize facts, but simply states them. Originally, matter-of-fact was a legal term meaning "portion of an enquiry concerned with truth or falsehood."