You may never notice if a mead is made with good versus great water; but, you will probably notice if it's made with bad water! Poor water selection can also lead to fermentation problems.
A lot of people are uncomfortable using the water out of their tap for making mead for one reason or another. Fortunately, water can be bought cheaply at the grocery store.
While distilled water is viable, it is not typically recommended.
Distilled water contains extremely low amounts of free O2 and zero mineral content. Provided that you are rehydrating your yeast with a rehydration nutrient and providing nutrition from a source like DAP, Fermaid, etc, and provided that you aerate the must well before pitching. These aren't serious issues; but, they are worth mentioning nonetheless. If you're going to buy water, there's no reason to work against yourself.
This will be the same price, or cheaper, than distilled water and comes without the potential problems. So why not use this?
A lot of small towns and cities have pretty good tap water. If it tastes good to you and has a good quality report, there's no reason you can't use it. Remember that the final judges are your taste buds.
This is an annual report your water supplier is legally mandated to supply to their customers by July 1st of each year. You can generally find a copy of it on your water suppliers website. If not, you can request it from them directly. The CCR is the easiest way to determine if your water is fit to use (at least on paper) for mead making.
[This section needs to be expanded.]
Chlorine - Off flavors in finished product, potential problems for your yeast. This is easily removed by allowing it to sit exposed in a bucket overnight. It can be filtered out with a charcoal filter or even boiled off in a few minutes.
Chloramine - Medicinal flavors in finished product. Much less volatile than chlorine and therefore far harder to remove. They can be boiled off or driven off by exposure, but neither method is practical. According to experiments performed by A.J. deLange, boiling will take hours; exposure will take days to weeks. More expensive filtration systems generally unavailable to the homebrewers are situationally effective. The easiest way to remove these pesky molecules is to treat the water with potassium metabisulfite, also know as campden tablets. Generally, 1 tablet is enough to treat 20 gallons of water. Half a tablet is almost certainly sufficient for 5-6 gallons of water anywhere in the US. This is a relatively very small dose. Use the formula to determine the effective dose:
(x mg/l Chloramine + y mg/l Chlorine) / 6 = z tablets to treat 20 gallons of water
If you're using filtered well water, your taste buds will have to be your guide unless you're prepared to send a sample (or dozen) for analysis.
There are test kits that will allow you to determine a limited amount of information at home. Keep in mind that these kits may not always be as accurate or precise as a lab analysis.
If you have a pH meter, you can make some broad determinations using that alone. Hard water is generally more alkaline (pH > 7) and is indicative of more dissolved minerals. Soft water is generally more acidic (pH < 7) and may be an indication of dissolved metals. If the pH is not between 6 and 8.5, you have a significant reason for further investigation.