The wheels hold the tires, and the tires keep the car on the road.
Seriously now.
Tires work by causing friction against the road bed. The more friction the better the handling (more or less). Friction, or "grip" is created and altered in a number of different ways.
Those ways include:
Contact patch: the amount of the tires surface that is in contact with the road at any given time. Contact patch (static, not including cornering forces/tire deformation, and alignment, etc) is a function of the tires overall circumference, width, tread design, and pressure.
Pressure: Changing tire pressure is a great way to (if done in small increments) subtlely change the performance to "fine tune" a car's handling.
Sidewall height/stiffness: Generally speaking the shorter the sidewall, the stiffer the sidewall. The stiffer the sidewall, the less tire deformation occurs when cornering.
Tire Rubber compound: Simply put, how "sticky" the tire is goes hand in hand with tread design.
Tread design: Engineering a tires tread design is beyond me, to be honest, so I can't go into the specifics. Alignment affects this area of performance as much as it does contact patch.
Wheels affect your car also:
Weight of the wheel: Lowers your wheel horsepower rating by increasing the "rotational mass" of the system. Adds more strain the the steering system. Adds more strain to the suspension system. Adds more/faster wear to your wheel bearings. Adds more strain to the entire drive train: motor, trans, clutch, driveline(s), differential(s), axles, u-joints, and associated bearings.
With an increase in tire width you will see an increase in cornering capability, also a decrease in fuel mileage, and overall top speed by having more "frontal area", more on that in another post about aerodynamics. Widening the tires also puts more strain on the steereing components by increasing the static and rolling resistance of the tire.
Increasing the diameter, and therefore the circumference of the tire means that for every revolution of the motor the vehicle travels farther, numerically lowering your overall gearing ratio(numerically, from for example, 3:1 overall to 2.7:1 overall), but effectively raising, decreasing your car's ability to accelerate, theoretically increasing your top speed, so long as you have the hp to push it faster. Conversly lowering your overall tire circumference numerically raises your overall gearing, effectively lowering it, allowing you to accelerate faster, but lowering your theoretical top speed.
Seriously now.
Tires work by causing friction against the road bed. The more friction the better the handling (more or less). Friction, or "grip" is created and altered in a number of different ways.
Those ways include:
Contact patch: the amount of the tires surface that is in contact with the road at any given time. Contact patch (static, not including cornering forces/tire deformation, and alignment, etc) is a function of the tires overall circumference, width, tread design, and pressure.
Pressure: Changing tire pressure is a great way to (if done in small increments) subtlely change the performance to "fine tune" a car's handling.
Sidewall height/stiffness: Generally speaking the shorter the sidewall, the stiffer the sidewall. The stiffer the sidewall, the less tire deformation occurs when cornering.
Tire Rubber compound: Simply put, how "sticky" the tire is goes hand in hand with tread design.
Tread design: Engineering a tires tread design is beyond me, to be honest, so I can't go into the specifics. Alignment affects this area of performance as much as it does contact patch.
Wheels affect your car also:
Weight of the wheel: Lowers your wheel horsepower rating by increasing the "rotational mass" of the system. Adds more strain the the steering system. Adds more strain to the suspension system. Adds more/faster wear to your wheel bearings. Adds more strain to the entire drive train: motor, trans, clutch, driveline(s), differential(s), axles, u-joints, and associated bearings.
With an increase in tire width you will see an increase in cornering capability, also a decrease in fuel mileage, and overall top speed by having more "frontal area", more on that in another post about aerodynamics. Widening the tires also puts more strain on the steereing components by increasing the static and rolling resistance of the tire.
Increasing the diameter, and therefore the circumference of the tire means that for every revolution of the motor the vehicle travels farther, numerically lowering your overall gearing ratio(numerically, from for example, 3:1 overall to 2.7:1 overall), but effectively raising, decreasing your car's ability to accelerate, theoretically increasing your top speed, so long as you have the hp to push it faster. Conversly lowering your overall tire circumference numerically raises your overall gearing, effectively lowering it, allowing you to accelerate faster, but lowering your theoretical top speed.
Yeah, it's VERY noticeable when switching from a 235-70-15 (9c1 police wheel on b body ) to common 255-50-17 (impala) wheel. 
