DPI is most commonly used to describe the pixel density in printing.
DPI has the same meaning on a monitor as on a printer. i.e. number of "dots" per inch. Technically the term should actually be PPI (pixels per inch) on a monitor but DPI is such well known term that it is used for monitors as well.
Your screens 'DPI' remains constant.
No, lets take an example. The physical horizontal size on a 17" monitor is approx 14". If you use a resolution of 1280x960 the DPI becomes 1280/14=91 but if you use a resolution of 640x480 the DPI becomes 640/14=46.
Windows uses DPI setting to ensure that fonts will have the same size on the screen as they have on paper.
Example: a 72 point(*) font is 1" high when printed. When rendering the same font on the screen it should be built up from 91 pixels (at 1280x960) and by 46 pixels at 640x480. (And will be built up by 300 "pixels" on a 300DPI printer)
(*) Note that font size is expressed in "points" but these "points" have nothing to do with pixels. A point is a typographical term used long before computers with is the same as 1/72 inch.
It is true that LCD screens has a fixed DPI but that only applies if you don't scale the image to fit the screen, i.e. if 640x480 is displayed as a centered "window" with black borders.
Also have a look at the DPI settings in windows.
(Display properties/Settings/Advanced/General/DPI Settings/Custom Settings..)
You will see a ruler. The idea is that you lay a normal (physical) ruler on the screen and adjust the displayed ruler so that the inch markers on the screen matches the inch markers on the physical ruler.
Unfortunatly the DPI settings doesn't work properly in windows. E.g my laptop got a display of 1024x768 at 88 DPI but my desktop LCD got 1280x1024 at 96 DPI. Windows automaticly change the resolution when I connect the desktop LCD but the DPI setting is unaffected.