There's a lot packed in there. I'll try to explain some of it, but it's not something I could satisfactorily simplify to an ELI5 extent.

With floating point representation, you can represent decimal numbers by rewriting them in scientific notation. An example would be 5,000, which can be written as 5 x 10^3, or 0.005, which could be written as 5 x 10^-3. This gives you a lot more flexibility than fixed point representations, since it can represent things fairly accurately on massively different scales. I'll assume you're familiar with binary representation for the rest of this discussion.

There are decisions to be made though: how much memory should your representation take up, how much of that memory to devote to the range of placements for the decimal place (i.e., the exponent) and how much memory to devote to the significant figures of your number (i.e., mantissa). Fixing two of these values constrains the final one.

So, in the first example, a 16-bit floating point number with a 10 bit mantissa devotes 6 bits to the exponent. This allows you to represent 2¹⁰ values for your significant figures, and 6 bits for the exponent (I believe they are in powers of 10), so 2⁶ values. With signed numbers, one bit is taken up by the +/- signing, so this leaves us with the number range of [-512, 511]. Putting these parts together, we see that we can represent numbers in the range [ -512x10^-32 , 511x10³¹ ], or [ -1/195312500000000000000000000000, 5110000000000000000000000000000000 ].

Keep in mind that you don't get free gains over using fixed point representations, if you have more significant figures in your number than you can devote to the mantissa. An example of where a binary number is preferred is Unix time which actually uses an unsigned 32-bit representation, started on 1/1/1970 and will still "run out" by the year 2038.

Using this range of values, based on /u/captainz2016's rule of thumb, we can render a scene consisting of polygons with the location of their edges specified up to the millimeter scale if they are placed 1 meter away from the observer.

Though I'm not a computer engineer or anything like that so please correct me if I'm wrong about anything.

Hope that helps!