I am a little confused on this, I have been using tap water which seems to work(I don't know if there are some long time after effects). But someone recommended to use the water coming out from my A/C unit in my house. Is it so? Or I have to purchase the battery water specifically?
You should only use distilled water in to top off you battery. Anything else will contaminate the battery and cause it to fail prematurely.
When filling your battery, regular tap water isn’t going to cut it. Tap water contains minerals that are harmful to batteries, even if added in small amounts. This is particularly true for water softened by water softeners which contain chlorides. To be safe, distilled water is your best bet and is a much smaller investment than a new battery.
The waste water from an air-conditioning unit is distilled water and is safe to use to top up a car battery.
It's also good to fill steam irons, as it contains none of the stuff in tap water! Fluoride is only one chemical in tap water. It's also good for watering your plants and you can drink it too! Anything that could be harmful in A/C water will have been added to it in the collection process -- for example, a dirty container or dirty pipes. It leaves the A/C unit perfectly clean and toxin free.
A lot of tap water is contaminated to some extent with sewage due to underground pipes leaking in to each other. That is why fluoride is added: the story about you teeth is only part of the picture. Bacteria can't grow in an environment with fluoride -- its all about killing bugs in the water. In the UK, some of our tap water supply pipes are over 150 years old and are known to contain bacteria that the fluoride then kills.
Air conditioning waste water is actually safer than a lot of tap water! Since it is distilled, it's perfectly fine to top up a car battery with it.
I hope this clears up any differences about its use in battery's, however, it costs about £2 a litre to buy it and since you will only ever need to buy distilled water a couple of times in your life, then unless you own a garage and service vehicles it's not much of a money saver. Feed your plants with the A/C water; they will thrive. (Fluoride is not good for plants; it effects the chlorophyll process. Though this is denied by water company suppliers, science says it does slow the process down and they saw funny brown spots on green plants fed on tap water which can't be explained!)