Curtains make or break a room faster than almost anything else you hang on a wall, because they are the one thing that changes with the light instead of just sitting under it. A bare window looks fine at noon and bleak at seven in the evening once the sun drops and the glass goes black and flat. Fabric softens that moment. That is really the whole case for them.
They matter most in rooms where you sit still long enough to notice the light, living rooms, bedrooms, a reading corner, anywhere you spend a dark winter afternoon or a slow Sunday morning. In a sunny apartment they take the edge off a west facing window that turns the whole place into a greenhouse by four o'clock. In an older house with drafts, a heavier pair does double duty, pretty during the day and a bit of a windbreak once the temperature drops. Rented places benefit too, since curtains are one of the few changes you can make that feels permanent without touching a wall.
In an ordinary room, curtains work with what is already there rather than against it. They read best against plain walls and get lost against busy wallpaper, so if your walls are doing a lot of talking, keep the curtains quiet and let them pick up one color already in the room, a cushion, a rug, the trim. Hung a little wider than the window frame and a little higher than you think, they make the whole window look bigger, which is a cheap trick that works almost every time.
If you own none and are starting from nothing, go with a mid weight cotton or linen blend in a neutral, not sheer, not blackout, something in between that filters light during the day and still closes with enough weight to feel private at night. Sheers alone look nice in photographs and do almost nothing once the sun goes down. Blackout has its place in a bedroom but can feel heavy everywhere else. The in between fabric is the one you will not regret.
Good curtains age well if you treat them decently, a shake out now and then, a wash on gentle when the label allows it, kept out of direct sun as much as you can so they fade evenly instead of in stripes. Linen softens and gets better with time. Cheap polyester blends tend to go limp and a little shiny after a year or two, which is the one place worth spending a bit more.
Hang the right pair and a room you already know well starts to feel finished at both ends of the day, not just in the daylight hours you planned for.