Water may not seem like a big deal when you are sick because typically you are more lethargic, but it may be more of an issue than when you are well.   If you are vomiting or have diarrhea this is even more true.  Vomit and diarrhea both contain a lot of water, so you need to replace it and then some when you are sick.

Since water participates in almost every process in your body, you must have a plentiful supply for your body to function at its optimum; and that includes your immune system.  When your body has plenty of water, it is better able to battle illness.

Oftentimes it is difficult to consume much when you are sick.  Eating very little is not a big deal because your body has energy reserves, but water diminishes very quickly.  When I am sick I usually drink about 3 times as much water as normal (if I can), even though my activity level is much lower.  When I get sick (which is rare) it usually lasts about half the time it does for everyone around me.  This is not strictly due to my water intake, but it plays a large role in overcoming and recovering from illness.

If you want to be a healthy person when you are sick, the only way to do that is to get better.  Consuming plenty of water is a huge part of that.