*There something that bothers me for a long time: Can someone explain that dpi is so important for rendering?

*DPI means Dots Per Inch, and is a term used in Printing.  It's a measure of how much ink is used while printing.  An image that is rendered at 300DPI actually has 300/72 more pixels than an image rendered at 72 DPI.

In other words let's say you render an image of 1000 x 1000 pixels at 300 DPI.  If you then open photoshop; load the image, and convert it to 100 DPI, then the converted image is now 3000 x 3000 pixels(without any loss of detail)

You have a printer, whose resolution is fixed at, say, 72 dots per inch (DPI), a dot being the smallest paper space that it can fill with its ink or toner.
Then you have an image set up to 300 DPI, fine.
Do you think your printer would produce a 300 DPI image? I don't think so :)

and

I entirely agree. But if you look back the original question wasn't printing related. The actual question was:

You don't have a printer set to print at 72 DPI.  72 DPI is the resolution your monitor uses.  A cheap inkjet printer, now a days, is at least 720 x 720 DPI - 1440 x 720 DPI, or more.