There is a whole science to this. Softer water for lighter pilsner style beers, harder water for heavy stout style beers. Pure water is not recommended used for brewing because some amount of the three ions (sodium, chloride, and sulfate) is generally considered necessary for some part of the flavor profile.
 
If by "pure water" you mean something like distilled water then there are two answers here. If you are extract brewing then "pure water" is OK. But if you are brewing all grain recipe then "pure water" is not OK.
 
Ions in brewing water help setting the mash pH to optimum levels and will impact the flavor of the beer. In extract brewing, the mash has already been done for you, so you can use de-ionized water. The extract itself will have mineral ions in it, residual from the mash, and that ion content will probably be fine from a flavor perspective.
 
The main point is to use some sort of filter if you are unsure about your tap water, or buy some water, and start brewing. 
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