Long and short scales are ways of counting big numbers. Normally we count like this: one, two, three, four, etc. But when we count really big numbers, it's easier to use a long or short scale.
In a long scale, every time you get to one hundred (100), you start counting all over again with a different word. So one hundred (100) is called one “hundred”, two hundred (200) is called two “hundred”s, and one thousand (1000) is called one “thousand”. This keeps going until it reaches one million (1,000,000), which is called one “million”. After that, it follows a similar pattern, with one billion (1,000,000,000) being called one “billion”, one trillion (1,000,000,000,000) being called one “trillion”, and so on.
In a short scale, each word is ten times bigger than the last word. So one hundred (100) is still called one “hundred”, but after that it starts getting bigger. Two hundred (200) is called one “thousand”, three hundred (300) is called ten “thousand”s, and one million (1,000,000) is called one “million”. After that, it follows a similar pattern, with one billion (1,000,000,000) being called one “billion”, one trillion (1,000,000,000,000) being called one “trillion”, and so on.
So long and short scales are just different ways of counting really big numbers.