When creating something new, be it for print, web or otherwise, you can’t go past knowing who’s going to using your end product. I’ll be the first to love designing something for the sake of doing so, though isn’t the most constructive approach to any design problem. What actually matters most, in any instance is nailing the brief from the outset. My means for this are simply that if you know what you want to achieve at the beginning then your end product is far more likely to fulfil this.
As an example, I designed myself a calendar for this year. My design was limited by the abilities of what I intended to print with. In my case, I have an A3 printer at home so I can design my product to look and feel pretty similar to one that you would buy off the shelf. Were I designing this for others to print at home, I’d have to reconsider my design altogether – average Joe simply doesn’t have an A3 printer at home.
The same goes for websites, considering your audience and how they might likely interact with you is pivotal to the design process. Are they seeking you out on their phones or iPads? If your site is only awesome on a desktop machine but your audience like to surf the web on mobile devices, it may be time to consider serving their needs.