HIghlights can give flat hair definition and the appearance of volume. They can be used to give hair an outdoorsy look, as though the sun has bleached a few strands, or they can be used in thicker, bolder stripes for a fun look. Highlights don't have to be simply bleached. They can be subtle or vivid colors. It's all a matter of personal taste.
For black hair, classic blond (bleached) highlights can seem harsh and may stand out more than desired. For a subtle look, consider dying in highlights (or streaks) in a shade of brown. The deeper the brown, the softer the highlights. Lighter brown, bordering on blond, will show up more vividly. Consider chocolate browns.
Red and black look great together. For subtle highlights, choose from the auburn shades. For something bolder, consider the burgundy reds or the bright, vivid cherry reds. There's also strawberry (or reddish blond) to consider. Out in the sunlight, red tends to reflect; so whatever red you choose, it will be more vivid in natural light than artificial. So consider that when choosing your color.
Instead of just using scattered highlights, consider widening a few into streaks for a mix. You can stay with the subtly of brown or the contrast of red. Or you might consider the wilder colors used in hair today. Because black is so basic a color, any color will stand out and offer a wild look. Perhaps a streak of blue suits you, or purple or orange. But for black, if you want a little wild, but not quite so noticeably wild, consider putting in very blue-black highlights, the blue that's so dark it's almost a black.