You catch malaria by being bitten by a mosquito that has malaria parasites living inside it. It doesn't hurt the mosquito. When the mosquito bites you, the malaria parasites go from the mosquito's mouth into your blood and then they reproduce and make lots more parasites inside your body. If you have malaria, you start to get fevers and you feel first very hot and then very cold. About one out of every ten people who caught malaria died of it, especially if they were kids.
More people have probably died from malaria over the last several thousand years than from any other disease that you can catch. Malaria parasites probably first began to infect reptiles in West Africa and Central Africa, at least a hundred and fifty million years ago (150,000,000 BC), in the time of the dinosaurs. Africa was warm and wet and so there were a lot of mosquitoes there. When mammals came along, the mosquitoes bit them too, and they also got malaria. But based on genetic evidence, people probably didn't start getting malaria until about 8000 BC, when people in Africa started to live in big enough groups for the disease to spread easily.
From its beginnings in Africa, malaria slowly spread all over Asia and Europe. Sumerian and Egyptian doctors from about 1500 to 2000 BC described fevers that sound like malaria, and DNA evidence from Egyptian mummies shows that they had malaria around 1500 BC. In India, people seem to have been catching malaria by 1000 BC, and by 800 BC the Indian surgeon Susruta knew that you caught malaria from insect bites. Malaria was common in China by 1 AD or so, when it was described in a Chinese medical text, the Neijing. By the 300s AD, the Chinese doctor Ge Hong also suggested a real treatment for malaria - the qinghao plant, which is still one of our main medicines against malaria. Malaria seems to have infected ancient Italy and Greece during the Hellenistic period (about 500-1 BC) - it may have killed Alexander the Great - and then northern Europe not until the Middle Ages, about 1000-1500 AD. The Holy Roman Emperor Otto II was an early victim. Europeans, however, did not understand either the cause or the cure. Rice farming, in both China and Europe, turned out to be an excellent way to spread malaria, because of the standing water in the rice paddies. This led to big arguments between rice farmers and public health officials who were trying to stop malaria from spreading.