Water, water, everywhere,
And all the boards did shrink;
Water, water, everywhere,
Nor any drop to drink.

The Rime of the Ancient Mariner
Samuel Taylor Coleridge, 1798

I was toddling around an internet winemaking forum this past week when I was suddenly reminded of Sam Coleridge's epic poem of touring Antarctica and a birding expedition gone wrong. Coleridge's poem is open to many interpretations (my own is that it's an examination of original sin, plus his wicked habits and hatred of birds) but everyone remembers the 'water, water' line.
The question that prompted me to re-read Coleridge was how minerals in water affected the character of wine. There was a lot of confusion about the role water plays when you make wine from kits.
All wine kits require the addition of water to reconstitute the kits to their 6-US gallon starting volume. 4-week and value-priced kits need a bit more water, since they contain more concentrate, while bigger, 6-week and Limited Edition kits need less water, since they contain more single-strength, unconcentrated juice.

Why the difference? It's fundamentally connected to why wine kits exist in the first place. Forty years ago, research showed that at a certain sugar content (known as 'Brix', expressed as a percentage of sugar by weight) and a known pH, fruit juices became shelf-stable at room temperature. Pure juice from crushed grapes always spoils quickly, being less than 28 Brix, no matter the pH. Boost the sugar content above 34 Brix (by removing water) and ensure the pH is below 3.4 and the juice will last at room temperature for a year or more with no degradation.
This observation caused the creation of the modern wine kit, in all its glory. It's inescapable however, that unless a bucket of juice is shipped frozen, it's always already on its way to fermenting within weeks of packaging. Luckily, we've got Master Vintner to keep us supplied all year long!
The retail water industry has made a big hairy deal about the quality of water in North America. So much so that many people assume they must buy bottled water to add to their kits. Unless your tap water is phenomenally awful, with permanent hardness, high iron levels, or wretched smells and flavours (so bad that nobody drinks it), then it's fine for making wine from kits.

I don't personally use any kind of bottled water. My reasons are several:

1. I hate paying for something that's readily available for free
2. Plastic water bottles are made from oil and require energy to produce, ship and store.
3. Nobody can prove bottled water is better than tap

In a blind tasting, Decanter Magazine judged two dozen different waters, and majority of the tasters preferred tap water from the water fountain located outside the conference room where the tasting was held. The panel was made up of sommeliers and Masters of Wine, and was done blind. It's pretty telling that local tap water placed third, while $100/litre H2O in a crystal-studded bottle placed nearly last.
Municipal water treatment is a fascinating topic. The process for treating tap water usually involves pumping it into storage tanks, screening out lumpy stuff (leaves and sticks), adjusting the pH (if it's too acidic, it can leach metal from pipes), a fining step (just like that which wine), filtration and finally disinfection.
(Also? A quick shout-out to water engineers. Through their efforts to ensure a supply of clean, safe water throughout history they have saved more human lives than anything except covering your mouth when you sneeze and washing your hands frequently. If you know a water engineer, salute them and honor their service to humankind.)
Disinfection is what throws people. It's natural to assume that because you can smell chlorine or chloramines in your water, it's going to affect the wine. Both of those compounds are essentially bleach, and are there to kill bacteria that might affect your health. They're added in the treatment facility, but can also be used by your local water authority right at the mains to treat a section of pipe that may have been broached, or disturbed, which can stir sediment into suspension and make it possible for bacteria to make it into your tap.
The good news is that your Master Vintner kits all have a small amount of sulfite. Sulfite is present on all grapes, even ones that are grown organically. When we make our kits we add a tiny bit more, around ten part per million. We do this to prevent oxidative browning and to suppress any spoilage organisms that might cause the wines to ferment during shipping and storage.

When sulfite comes into contact chlorine in water the sulfite binds to them instantly, forming stable chloride salts like potassium chloride or sodium chloride--the same thing as table salt. When sulfite binds to 100% of the legally allowable levels of chlorine in municipal tap water added to a kit, you wind up with about two grains of table salt per 23 litre batch. That teensy amount does not have any effect on your wine kit.
For the most part it's safe to rely on your municipal water authority to take care of your water needs: there are federal guidelines covering how and what can be in water, and they're legally obligated to provide you with a report on your water quality when you request it.
On the other hand, if you're in an unincorporated area, or on well-water, you need a laboratory assessment of the water to make sure it's not contaminated with minerals like iron (the enemy of winemaking) or high in bacteria.
Keep in mind that if you're from somewhere like my ancestral stomping grounds in the Canadian Prairies your water will be hard enough to break rocks and smell like it's been drank once already--that's the exception that shows you may want to choose bottled or filtered water to make up your wine. My rule of thumb? If strangers to your town will drink the water without remarking on it, it's almost certainly good enough to make wine kits with.