Twenty-four blackbirds is big-endian. 24 (twenty-four) = 2×10 + 4×1. The leftmost number is the 'biggest' (big end first). 3124 (three-thousand, one-hundred and twenty-four) would be 3×1000 + 1×100 + 2×10 + 4×1. This is the decimal, or base10 system that most people in most countries learn first these days.
Four and twenty blackbirds is little-endian. 42 (still twenty-four) = 4×1 + 2×10. The leftmost number is the 'littlest' (little end first). 4213 (three-thousand, one-hundred and twenty-four) would be 4×1.+ 2×10 + 1×100 + 3×1000. Note this is not the normal way of doing things in the analog world. But, this is common in the digital world.
This applies to the way all data is stored in a computer, not just numbers. And of course most computers use a hexidecimal, or base16 system.