Tyre and rim sizes 101:
ISO sizes, which are the definitive numbers, are small & large numbers like 559x17 (rim) or 37x559 (tyre). The numbers are dimensions in millimetres.
The important number is the larger of the two; in this case, 559 (mm).
This is the diameter of the flat shelf inside the rim that the tyre bead sits on. Both tyre and rim have to be the same size, or either you won't be able to fit the tyre, or the tyre will blow off the rim when you try pumping it up, if it's not fallen off before you get that far.
Road bikes and 29-er mountain bikes use 622 mm rims and tyres
27.5" mountain bikes (aka 650B) use 584 mm rims and tyres.
The smaller number is the interior width of the rim, or the exterior width of the tyre.
These are more flexible, but as a rule of thumb the minimum tyre width for a rim would be the next standard width wider than rim width plus 6 mm (6 mm being the typical difference between interior and exterior rim width), and the maximum tyre size would be double that.
So, in the case of your 17 mm wide rim, the narrowest allowable tyre would be 25 mm wide, and the widest 50 mm. For off-road use, you might like to increase both min and max sizes a little.
Inch sizes are historical, confusing, and best ignored.
Back when rims were made by the tyre makers, tyres were sized by outside diameter, and were generally a nice round number, as was the width/height (bike tyres are circular in cross section on the inside).
So you'd get fat 26 x 2" tyres, and thinner 26 x 1 1/2" tyres, both of which were 26" diameter on the outside, but which used different rims. The 2" wide tyre would use a rim that was 26" - (2 x 2") = 22" across, and the 1 1/2" tyre would use a rim that was 26" - (2 x 1 1/2") = 23" across. If you convert 22" and 23" to mm, you get, lo and behold, 559 mm and 584 mm.
The French did similar, but their nice round tyre diameters were 700 mm, 650 mm etc, and they referred to narrow, medium, wide, and wider tyre widths as A/B/C/D rather than giving exact widths (I think there was a little flexibility in the A/B/C/D tyre widths, so they got the same size rims as the British inch sizes).
Later on, rims were made by other companies, and the tyre manufacturers had to make tyres to fit existing rims, so you'd see tyre sizes like 26 x 2 x 1 1/2", which was a 1 1/2" tyre to fit a rim that was originally for a 26 x 2" tyre.
When mountain bikes came along, the Americans correctly decided that this was all too complicated, so they standardised on the rim size for a 26 x 2" tyre (because that was the readily available fat tyre size at the time), dropped the 2" bit of the original specification, and changed from fractions to decimals, so your 26 x 2 x 1 1/2" tyre became a 26 x 1.5" tyre.
For wider use, confusion still reigned, because there were several different 26" sizes, and more than one of several of the other whole inch sizes. You'd even occasionally get tyre makers putting the wrong numbers on the tyre.
Therefore the standards committee (ETRTO) came along and said "thou shalt quote tyre and rim sizes in millimetres, as follows...", and the tyre and rim makers did, or at least made the millimetre sizes available by putting them on the tyres and rim labels. The only remaining task is to get all the bike shops to use them.
Pressures:
The 1.5" and 2.1" on your rim label aren't maximum and minimum tyre sizes as such, but the sizes at which the maximum pressures to the right apply. At any given pressure, the wider the tyre, the more the pressure tries to push out the rim flange. So, if you have a 1.5" tyre fitted, you shouldn't use a pressure higher than 90 psi/6 bar or you are risking rim failure, but if you have a 2.1" tyre fitted, you shouldn't go higher than 60 psi/4 bar.