Tomato water is a Umami. Whats an Umami? Okay, lets start there. Umami is the fifth flavor discovered by the Japanese in 1908 and found in a variety of foods that are rich in glutamate like tomatoes (paste, dried, even ketchup. Think Italian foods- got it?), soy sauce, anchovies, truffles. Parmesan Cheese, porcini mushrooms, soy sauce, balsamic vinegar, fermented sauces from fishes, and sauerkraut. Vegetables like leeks, and cabbage along with soup stocks, especially chicken are perfect flavor enhancers . All GOOD stuff, and who cooks like this? The French, Italians, Japanese, Greeks almost all countries outside the US that doesn’t use processed foods out of a box with industrial glutamates like Monosodium Glutamate for taste. Learning to cook is the very best thing anyone can do for themselves.
Tomato water involves extraditing the water from over-ripe tomatoes. In fact, the best tomatoes are the ones in the “please buy for a buck” box next to the cash register at your Farmer's market. The tomatoes that have fallen off the vine in your garden are prime candidates or if all else fails, buy some juicy ones that are soft to the touch.
Cut away any offending section, slice into quarters and place in a 2 or 3 qt sauce pan or pot and set on medium heat to soften and slightly stew your bounty.
Mash tomatoes with the back of a wooden spoon and drain in a fine mesh metal strainer. The first strain will remove the skins and seeds, adding a cheesecloth to a second straining will clear the water to a light reddish hue ready to cook or slip with a dash of pepper. Not as rich as a tomato juice but a million times purer and enriches the flavor of what ever you are cooking from soups & sauces to cocktails.