Precisely what the word means. Medically sensitive. Or maybe "fragile". There are many kinds of foods that can be threatening for your health if you are oversenstive to that kind of food. Nuts for example is very extremely famous for that. When it comes to nuts it even goes so far, that you can get yourself killed for eating them when you are oversensitive to them. (that is also why warning about nuts are sometimes present on ... tadaa.. bags of nuts).
Raw fish, one of the main ingredients of sushi, is hard to keep free of bacteria and other stuff (as when you bake, fry, grill, etc. stuff all bacteria will normally die in the process due to overheating), and if your resistance to that is not up to par, meaning you are sensitive to that, you can get yourself very extremely sick from eating sushi, and yes in extreme cases you can even die.
In in theory all kinds of food can make you ill or even kill you, but some kinds of foods have a higher chance of health trouble, and then there are also higher amounts of people affected. By law these people should always be warned that they may be about to eat something their bodies will very likely not agree with. Raw animal products (which sushi is) are very dangerous to those with a weaker boy in general.