I'm brand new to Inkscape and I'm trying to feather the edges, or create a gradient on the border of a geographic area for a map I'm making. The desired effect looks something like this:
If you'd prefer a fuzzy border inside the land's borders, rather than outside, try this...
Create your vector land shape and give it a fill colour and no stroke
Duplicate this land shape twice (press Ctrl + D twice) so that you have three copies. One copy will stay as the original land shape, one will create the border, and one will be used for clipping.
Click the topmost land object to select, and (optionally) remove the fill colour, then give it a stroke, colour of your choice. Inkscape puts half the stroke width inside the shape, and the other half will extend beyond the shape edge, so a 50px stroke will give a 25px 'border' inside the shape.
Now give this border a blur. How much depends on your stroke width and personal taste, so play around with the blur slider in the Fill & Stroke panel. If you feel your blur isn't 'wide' enough (or is too wide) go back and change the size of your stroke, making it bigger or smaller as required.
Once you're happy with the border effect, click it once to select, and press the PageDown button to lower it. With the blur/stroke object still selected, hold shift and press the topmost land shape that should be showing. With both selected, on the menu, go to Object / Clip / Set. This will hide the blur outside the land shape and leave a nice, coloured border inside.