Your simple processors: PICs and AVRs, the 6502 and Z80 from the BBC Micro and ZX81, and even the 8088 and 80286 from the original IBM PC and PC/AT dealt only with whole numbers. There were 8 bits to a byte and 16 bits to a word. With a byte you could count from 0 to 255, or if you looked at them another way, -128 to +127. With a word you could count 0 to 65536 or -32768 to +32767. If you put two words together you could count up to 4 thousand million. But you could not count fractions very easily. You could decide to move the decimal (or binary) point a bit, making a byte maybe 0.0 to 25.5, but that cuts your range down a lot.
So people invented floating point. It has a "mantissa" which is all the numbers, and an "exponent" which is where to put the (binary) point. Using 4 bytes for one floating point number you can count up to over 100,000,000,000,000,000,000,000,000,000,000,000,000 and down to 0.00...1 (with the same number of zeros).
The problem is that to do that you need to write a lot of software. To add two floating point numbers you need to shift the mantissas and adjust the exponents until the exponents are the same as each other and only then can you add the mantissas. Multiplication is easier and you only have to multiply the mantissas together and add the exponents together. All that software takes time to run; it is ten or a hundred times slower than adding or multiplying whole numbers, which the processors already know how to do in hardware.
So a processor that knows how to do floating point itself is obviously going to be faster. The PC got that at about the time of the 80386. The ARM got it in the v7 variant (IIUC), but there is an option to have it in the v6 variant. The RaspPi uses a ARMv6 that has hardware floating point support. However the existing Linux distributions all assume that an ARMv6 has not got hardware floating point support and therefore they don't use it. All of the floating point work is done in software (soft floating point). It was necessary for the Raspbian team to build a Linux variant that did the floating point work using the hardware (hard floating point).
That's basically it; there's another few wrinkles in there to do with exactly why a complete new distribution is needed, but that gives you the idea.