There are standards which define what the representation means so that across computers there will be consistancy. Note that this is not the only way to represent floating point numbers, it is just the IEEE standard way of doing it. S, E, F all represent fields within a representation. Each is just a bunch of bits. This is the sign of the number.
E is an exponent field.
The E field is a biased-127 representation. Computers that did not use this representation, like those built before the standard, did not always use a radix of 2. It is in a somewhat modified form. There are 23 bits available for the mantissa. For the standard form, it needs to be in biased-127 form.