In a nutshell
A computer stores every number as a fixed string of bits, so it needs agreed rules for what those bits mean. For whole numbers the standard is two's complement: it gives the leftmost bit a negative value, which lets one circuit add both positive and negative numbers, and you negate a number by flipping every bit and adding 1. For numbers with a fractional part, IEEE 754 splits the bits into a sign, an exponent, and a mantissa — essentially scientific notation in binary.