What does 26x1.5/559 mean?
 

26" diameter ?
1.5 tire height
What is the 559 ?

https://cimg9.ibsrv.net/gimg/bikefor...178a60a82d.png

559mm is the diameter that the tire bead sits at. This is the same as the "26er" wheel size that dominated on older mountain bikes.
1.5" is the nominal inflated width of the tire (inflated tire width can vary a little depending on the width of the rim it's mounted on).
So this tire mounts on a 559mm BSD ("26er") rim, and it inflates to around 1.5" wide, which is about 38mm.

The "26" is a marketing term very roughly based on the diameter of the inflated tire, in inches. But be careful:
https://www.sheldonbrown.com/26.html

...
...it's the standardized bead seat diameter. In your picture, for that size rim, it's 622. But that's a 700c rim, so the diameter is bigger.

There are several versions of 26" tires. The 559 is diameter of the tire in mm

Here is a link that might help you understand this

https://www.modernbike.com/iso-sizes-for-bicycle-tires-and-rims

It is what I consider the most common size of 26" tires

559mm = 22"
Add a nominal 2" of tire top & bottom and you have 26".
See Sheldon-
https://www.sheldonbrown.com/harris/tires/index.html

ETRTO is an international standard so tires fit rims made by someone else .. tire bead seat diameter 559-40 is another way to say which 26" x 1.5"..

It’s the diameter of the rim, not the tire. It’s the diameter of the bead for the tire.

The ETRTO size would be 38-559

ETRTO is the European Tire and Rim Technical Organization. ETRTO was the organization that brought standard nomenclature and defined sizes to the chaos of bicycle wheel and rim sizing in the past. A while ago the International Standards Organization (ISO) took over the job of defining bike wheel standards from ETRTO so you will see bike wheel sizes stated as ISO sizes which are identical to the older ETRTO sizes. So an ISO 622 rim is the same as an ETRTO 622 rim.

"Chaos" is exactly right. There are something like 10 or more different "26 inch" tire diameters among the various old systems: https://www.sheldonbrown.com/tire-sizing.html ISO/ETRTO sizes are simple and explicit.

What does 26x1.5/559 mean?
You have a tire that has that on the sidewall? Please post a pic. This will be the first time I ever will see a bicycle tire manufacturer prominently display something useful for tire size. Though not a true ISO size, it sure helps!

26" diameter ?
Outer circumference of the tire. But only very general and rough. Width of tire can very the circumference a lot. There are 26" tires that won't fit your wheel. So it's really a useless number to know. More to do with marketing and salespeople that aren't technically or engineering oriented.

1.5 tire height
Roughly, also roughly the width.

What is the 559 ?
BSD Bead Seat Diameter if you know this number you are well on your way to determining what other tires may fit your rim or what rims will fit the tire.