When the Old course at Stonewall opened, the GAP rating team came out and gave it a slope of 128 or some such. The founders howled in protest, suggested it was a much tougher scoring course than others locally that had higher slopes, and asked for it to be re-rated. It's now at 136, with three or four back tees that weren't there originally.
I rated about 150 courses in Oregon and Western PA over the years and am hoping to get back into it next year in NJ.
The funny thing about that is when if either the course rating or the slope increase your handicap will go down. If you average 80 on a course with a 70.0 rating and 128 slope, you are not as good a player as if you average 80 on a 71.0/136 course.
I can't tell you how many times I showed up at a course and had a member there tell me how his course is a lot tougher than the rating shows. I then explain that to him and he immediately wants the ratings lowered so his handicap will go up.
You cannot judge the difficulty of a course just from the slope and to do so is a big mistake.
As Michael pointed out, the slope is just the slope of the line of the difference between the course rating and the bogey rating. As an example working the formula backwards to get the Bogey Rating from the Royal Dornoch scorecard:
Yellow Tees: Rating 71.1, Slope 129 yields a Bogey Rating of 95.1White Tees: Rating 72.6, Slope 134 yields a Bogey Rating of 97.5
So, while the Scratch Course Rating goes up 1.5 strokes from the Yellow to the White, the Bogey Rating goes up 2.4 strokes that .9 difference changes the slope from 129 to 134.
I'll note that while it is extremely rare, it is possible for the longer tees to have a lower slope than the shorter ones. This happens occasionally when the bogey golf might not be forced to layup from the longer tees or might have most of the greens just beyond the length he can reach in regulation from those tees whereas he could reach them from the shorter tees with a much longer shot.
As others have said, the Effective Playing Length (yardage plus things like wind, elevation change etc) of each hole makes up 90-95% of the Scratch and Bogey Ratings. Of the remaining 5-10%, most of that comes directly from measurements and tables and is not subjective. The actual amount the rating team can subjectively determine is very small.