For an intro to DPI, try the
>Wikipedia< (the article is informative, but a little opinionated, surprise surprise). In bitmap-based computer graphics, DPI is little more than a suggestion. A 1000x1000 pixel image at 72DPI has exectly the same number of pixels and hence detail as a 1000x1000 pixel image at 300DPI. The 300DPI image will tend to appear smaller however because of the suggestion that each pixel be printer/displayed 1/300 of an inch apart.
For your application, if the brochures/signs are going to be professionally printed, then aim for a very large image size - 3000x3000 pixels (bitmap images) or A4 at 900DPI (vector-based graphics) - unless you happen to know that the signs will be quite large - in which case you may need to up the detail even more.
If the stuff is going to be printer in-house, then you could ask the client what the maximum resolution and paper size is of her best printer. Then you can target the image size to that printer. Feel free to post back if you need a hand with the calculations.