The tomato is the edible berry of the tomato plant (Solanum Lycopersicum) which is usually red, but there are certain cultivars with other colors as well (green, yellow, brown or even black tomatoes).
Tomatoes are botanically classified as berries (fruits) but they are commonly used as a culinary vegetable ingredient, as part of a salad or main course of a meal, rather than as a dessert, unlike other fruits which are usually much sweeter.
Tomato Paste is made by cooking tomatoes for several hours to reduce the water content and straining out the seeds and skins, then cooking the liquid again to reduce the base to a thick, rich concentrate (paste).
Tomato paste is used to impart an intense flavor (particularly the natural 'umami' flavor) and color to many various dishes, such as pasta, soups, or braised meat, being a natural (sometimes organic) red vegetal food colorant.
Similar to tomato paste there is also tomato ketchup. While tomato paste is rather used as a base for cooking, tomato ketchup is a sweet and tangy table condiment or sauce made from tomatoes, sugar, and vinegar, with seasonings and spices.
References: Read more about Tomato on Wikipedia