dpi = dots per INCH
so it's about clarity (resolution)
if a picture is 10 dpi it's the same size as one at 300 dpi ... but the blocks of colour that make it are bigger ... so it will be less well defined 10x10 = 100 as opposed to 300x300=lots and lots
.. you can take a pic that's 10 foot x 10 foot, and reduce it in size to 10 inch x 10 inch by throwing away some of the blocks - and it will still be recognisable (like seeing it at a distance)
but with only 100 blocks ... make it bigger and you still only have 100 bits of info to work with
a square of colour can be 10 or 10000 dpi and it's still a square
but where 1 colour becomes another - ie a gradient from black to white or curvy it will be smoother using more shades of grey or dots
if the flag is a cross + each block could be a single pixel and the crossover will be sharp
but if it's x the crossover will look blocky with lower numbers of blocks (resolution)
o...o
..o
o...o
pros will "overblow" pictures so a 300x300 block is drawn at 1200x1200 or more (pro quality is 2400x2400 so they'd work at 9600x9600 or more.
so to answer your question (at last!!)
the simple answer is - draw it bigger