When a microprocessor or microcontroller needs to execute a lot floating-point calculations, there are three ways to carry this out:
1) In software i.e. floating-point library
2) An FPU which is integrated intro the microprocessor/microcontroller
3) An FPU in a separate chip
Choice 1, doing it all in software, may be the only option if hardware FPU's are not available. A software solution will be 5-10 times slower, or even worse depending on the register size of the processor. I am currently doing a project which requires some 32-bit floating point math on an 8-bit HCS08. Doing that with an 8-bit accumulator is pretty ugly.
Choices 2 and 3 are pretty much the same thing, speed wise. One of the very first separate FPU's was the the 8087, a companion chip added to the 16-bit 8086, the great-great-great-great-granddaddy (or something like that) of the Intel or AMD 80x86 processor in your PC. It was developed for two reasons: Intel didn't have the capability at the time to include the FPU on the same chip as the processor; and this allowed it to be sold as an option -- the 8087 initially cost $150 just by itself. Computer makers put a socket next to the 8086 processor (or 8088 with an 8-bit data bus and 16-bit address bus, which was in the very first IBM PC model 5150) so a consumer could add an 8087 later on.
The 8087 had something like 60 different instructions. If there was no 8087, the 8086/8088 actually trapped the floating point instructions codes and emulated them in software. It could handle 32/64 bit floating numbers, and used an internal 80-bit register for calculations. It's floating point format was the basis for the IEEE 754 floating point standard, which is now used by all other FPU's and floating point software libraries.
Besides the typical floating point operations like add, subtract, multiply, and square root, it could do exponential, logarithmic and trigonometric calculations.
The FPU for the 80x86 was a separate chip up through the 80386/80387; from the 80486 onwards it was integrated into the processor. The advantage of having the chip as part of the processor, is that you don't need to have any extra leads (i.e. pins) between the processor and the FPU to control its operation. Outboard FPU's also shared data, address and other control lines with the processor, but those were already there to handle external memory.
There also were separate FPU chips for the 68000, and the early MIPS and ARM processor which did not have integrated floating point. Now both MIPS and ARM processors (in addition to the Intel 80x86 line and others) have FPUs built into the chip. The advantage of course is both cost and space on the PCB.
I am not aware of any 8-bit microprocessor or microcontroller that includes an FPU (external or integrated), except for the Intel 8232, designed for the 8-bit 8080.
I am also not aware of any microcontroller that has a separate FPU available for it, since microcontrollers generally don't have their address and data busses brought out to external pins like microprocessors do. However there is no reason not to include an FPU integrated into a microcontroller, like some ARM's do.
Whether you have a hardware FPU, or need to use a floating point library, in almost all cases this will completely transparent to you, since you just declare a variable to be floating point (float or double keywords in C for example), and the compiler will generate the appropriate instructions to either call the library or use the FPU. You may not to set up your compiler options though to inciate you have an FPU.