Draw is the resistance you feel when you puff on a cigar. If the draw is too tight, you have to work hard to get smoke; if it is too loose, the cigar burns hot and fast. The cause is almost always construction: how the filler was arranged (entubado or accordion), how hard it was pressed in the mold, and whether a vein or a lump is blocking the air.
Storage also affects the draw. A cigar kept too moist swells and can draw tightly. A dry cigar can draw very easily and taste like paper. See relative humidity and humidor.
A cutter that crushes the head will spoil a good draw, and so will biting the cap off. See cutter, guillotine, v cut, and punch.