Fats are foods which store energy in case you need it later. Everybody needs some fat in their food or they will starve to death. Some foods which have a lot of fat in them are avocados, sunflower oil, olive oil, nuts, meat, and butter and cheese. Fatty foods have a lot of calories, but they also help you feel full, and there's no evidence that eating them makes you fat.
In different parts of the world, people got their fat from different foods. In South America, fat came mostly from avocados and cashew nuts. In North America, people got their fat from buffalo meat and from sunflower seeds.
Around the Mediterranean Sea and in West Asia, people got fat mainly from olive oil, while further north in Europe it was mainly butter from cattle and fat from pigs. Further south, in Africa, most of the fat people ate came from palm oil and from sheep and cattle. In Central Asia, fat came from yogurt and cheese, while in India people pressed oil from sesame seeds, coconuts, and mustard seeds. Finally, in China, fat came from pigs and chicken.
Nutrition: What's in the Food We Eat, by Dorothy Hinshaw Patent and William Munoz (1992). Easy reading.