We are not referring to pointy objects thrown at a dartboard. This type of dart is regarding the sewing of fabrics to make clothing. Darts are often used on blouses (commonly for a woman's bust).
Darts are folds (tucks coming to a point) and sewn into fabric to take in ease and provide shape to a garment. They are used frequently in all sorts of clothing to tailor the garment to the wearer's shape, or 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.
Pleats or gathers in the fabric can be used as for the same purpose as a normal stitched dart. These are called dart equivalents.
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.