Essentially, it's primarily due to those two round pieces of rubber around your front and rear wheels that all those kilos of steel, propelled by so much horsepower are kept on the road and moving in the right direction. Yes, electronic aids, experience, skill and proper control of the right wrist help, but it would all amount to nothing without that double strip of rubber, each about a fist's width.
The right tyre pressure is vital for motorcycles. Not only for your own safety, but also to prevent premature tyre wear. Driving with the correct tyre pressure even has a direct effect at the fuel pump.
Correct tire pressure
It makes sense that most people don't have an industrial compressor or an air pump readily available at home. Living close to a petrol station with one of those isn't really necessary either. Nowadays, there are plenty of well-functioning and competitively priced devices that you can easily store in the cupboard or even take with you on the road.
That way you can always be sure that your tyres are at the right pressure, avoiding certain hairy moments.
Note: your manual will tell you the correct pressure and often it will also show on the rear axle or on the tyre. The pressure shown is always the cold tyre pressure. As your ride, the tyre warms up, which also warms up the air inside the tyre. Warm air expands and the pressure will increase because of that. In other words, it's best to check and inflate your tires before the ride. Make it a habit to check your tyre pressure every two weeks.