Although sewing a dart in fabric requires a pointy needle, this has nothing to do with the pointy darts that are thrown at dart boards.
Darts are folds, which are tucks coming to a point, and sewn into fabric to take in ease and provide shape to a garment.
The sewing darts are used frequently in all sorts of clothing to tailor the garment to the wearer's shape. They are often used for a women's bust. The darts on fabric can also be used to make an innovative shape in the garment. Fabric may be thought of as flat, and a dart has the effect of removing a wedge shaped piece and pulling the edges of that wedge together to create a shallow cone. This effect can be seen quite easily with a paper pattern by pulling together the edges of a dart intake as it would be sewn. Since fabric is generally more flexible than paper the fabric will shift around the apex of the cone and form a softer, but still curved, shape. In a garment a dart ends in a point at a full area of the body.
A dart in a flat pattern has two important properties: its point, the point in the pattern at which the dart aims or converges, and the intake, or the amount of fabric taken in or removed. Since the dart can extend toward any edge of the pattern without affecting fit, the length of the dart intake at the edge of the fabric is not a good measure of dart intake. Rather, the angle subtracted from the pattern by the dart is what determines the dart's intake.
Vertical darts are sewn from the bottom of the blouse to a point generally around the bustline. This type of dart may be found in the front, rarely in the back of a garment and are used by the garment maker to pull in the bottom of the blouse towards the wearer's waist.
Bust darts are short triangle folds that provide space for breasts such that the fabric under the breasts isn't hanging, rather is fitting closer to the wearer.