It is safe to say that most people use their tap water in their aquariums and probably couldn't tell you what's in it. The main parameters in water we generally test for are GH (general hardness), KH (alkalinity) and PH (potential of hydrogen).
Without getting too deep, what if tap water was really hard (a GH of 18) and you wanted to keep soft water fish, like discus?... well this is where RO/DO water comes in. Basically, the RO/DI process strips the water of virtually everything but the H2O allowing us to then add minerals back in to meet our needs. This gives us full control over the GH, KH and PH. To raise the GH in RO/DI water, I suggest a product called Seachem Equilibrium. To raise you KH, I would just plain ol' baking soda, which is sodium bicarbonate. If you need your PH to raise with your KH, use a carbonate (not to be confused with a bicarbonate) like calcium carbonate. With a little Equilibrium and baking soda, you have COMPLETE control over your water parameters. Its really that easy and can avoid TONS of issues that come with using municipal water supplies, or even well water. Both can be really unstable and uncontrollable.
So what is an RO/DI unit that doesn't break the bank? I suggest and RO Buddy by AquaticLife. I have had a 50gph unit for years now and never had an issue. At around $60 you can have complete control over your water parameters making sure your water parameters are rock solid. This connects up to a typical hose spigot or home faucet and can save you time and money from grabbing gallons of distilled water (which is the same thing) from your local department store.
To answer the question, do you need to RO/DI water? That answer is, only if you need to reduce the mineral content in your water, OR, if you want full control over your water parameters when keeping something like sensitive fish or shrimp. I hope this helps! :) Happy aquascaping to you all!