Tires (or tyres depending on who you ask) are a very dynamic part of a motorcycle. Many factors are working in unison where the rubber meets the road. To give an overview of the basics is probably all I am qualified to do as this is an extremely complex topic, but it is very important to realize that a tire is not just a tire and that it can only work properly when maintained properly.
I feel it is very important to remind everyone to inspect the presumably round black things on each end of your bike. As your bike sits for the winter the dramatic swings in temperature create contraction in both the rubber and the wheel , this and other factors result in low inflation by the time that first relatively warm spring day compels us to get the bike out. Wire spoke wheels lose quite a bit more air than tubeless setups do but never presume that you don’t need to check. Another factor that is to be considered is capacity, for example a narrow front tire will likely be low much sooner than the larger rear. This is noticeable on both motocross and cruiser style bikes with large diameter narrow front tires likely mounted on wire wheels.
If your tire is not properly inflated you stand to lose. Best case the tire will wear out fast and then you get to try a different one; likely dissatisfied with the longevity of the last tire. If the tire pressure is too low the flexing action of the tire as it roles will create too much heat in the tire quickly braking down the rubber and the bonds within the carcass of the tire. If a tire is over inflated the result is a reduced contact area (or footprint), since the footprint of a motorcycle is already very small it is a poor plan to give up any of it. A properly inflated tire does build some heat and the rubber compound used in the tire is chosen to optimize the grip and longevity of the tire for the category it was intended. Race tires are made of a compound that requires more heat than you can build on the street so don’t think it’s cool to put race compound tires on your street bike (I can speak first hand to this one.)
In off road applications much lower tire pressures are needed and the surface being traveled dictates the tire pressure needed. A muddy environment needs higher pressure as this opens the tread and allows the mud to escape so it can get a fresh bite on the next time around. On a hard surface you need as much of the rubber on the road as you can get so, low inflation gives a bigger contact patch so more rubber on the road.
It is popular to put a larger then stock rear tire on the back of your bike; this will have some negative effects and you should seriously think about the consequences for the small cosmetic gain. The motorcycle was engineered for a particular size of tire and any change in size will make a difference in the way the bike handles. Too big of a tire will create a slow transition in to a corner and if the tire is mounted to a rim that is too narrow for the tire the contact patch will be reduced rather than increased.
This is a very involved topic and I could go on for pages about the engineering and integration of your motorcycle and its tires but in short what I want to say is, put the right tires on your bike, maintain them, and ride happy.