Here's how I understand it, which is a little hand-waivy but, I think it's broadly correct. I'd be happy to be corrected, or somebody to explain it a little more technically but I hope this helps:
Ordered logistic regression works by modelling an unobserved continuous variable, that is put into its observed categories by the various cutpoints (which are called
Intercepts here). Any value below 10.04 on the unobserved variable will be assigned 0, between 10.04 and 12.66 will be assigned 1, and so on.
It uses a logistic distribution as the underlying distribution, the nice thing about that its units are log odds of increasing from category C or less to cateogry C + 1 or more. It is an assumption of the model that the coefficients are the same to move from 0|1-5 as it is to move from 0-1|2-5, (The 'proportional odds assumption'). Otherwise, you would need one coefficient for each variable and for each cutpoint. This is possible, but is a different model and is very hard to interpret.
So this leaves you with this interpretation (taking
log_pop1 as an example):
For a 1 unit increase in
log_pop1 there is a 3.13 increase in the log odds of the outcome being categories C or less compared to being category C or more. (whatever C is, this is the same, as I explained above)
But because it's difficult to interpret log odds, it is often best to take the exponent of the coefficients.
exp(3.134) = 22.97, so for a one unit increase in
log_pop21, the odds of being category 0 compared to categories 1-5, or from being categories 0 or 1 compared to being categoies 2, 3, 4 or 5, increases by a factor of 22.97 (because we have exponentiated the log odds, we now multiply the odds by
exp(coefficient) for every one unit increase in it).