This is such a novice question, and I'm almost embarrassed to ask. But, here I go ...
Say, you have a casting blank rated for 10 - 20 lbs. line. What does that mean?
The tips is soft enough so that a 10 pound test won't break when you set the hook?
But if you use lines heavier than 20 lbs, the rod might break?
Sorry in advance about this such an elementary question.

To me, they tell me what line would work best with that blank. As far as bass fishing goes, you think the rods they are using with braided line are really rated for the strength of the line? Take the rating as a way to pick the best blank for the line intended to be used with it.

You would be hard pressed to break a 10lb test line on a rod rated for 10lb line, despite how hard you set the hook. In fact, I think you would be hard pressed to break even a 6lb test line and maybe even a 4lb test line. If, by some freak of nature, you can break the rod using a 20lb test line, you are obviously setting the hook way too hard.

These ratings on rods do not mean the "line breaking strength" of the rod but are more like a recommendation for the line diameter (usually referring to monofiliment line) that will cast best given the action of the rod. Don't see them as referring to the rod "durability or strength" but as an indicator of the line to use to optimize the rods action.

These line ratings are nothing more than subjective ideas on which range of line is expected to be used the blank/rod. Some manufacturers have used them to list the line that wouldn't exceed to dead lift limit of the blank, but nearly any rod can be broken even with the rated line if you high stick the rod.

Unlike the lure weight ratings which are based on the actual power and action of the blank the line ratings are purely subjective. They don't really mean anything. Just like a blank listed under a category called "spin bass." It's just a suggestion as to what the blank might be used for.

.............

I think that this is an excellent question that is not addressed in any clear and concise way by the blank and rod manufacturers.
As Tom suggests th maximum load that a rod can take before breaking is a function of not only the weight but also the angle that the rod is held. The higher the angle the more the load is transferred toward the tip of the rod or toward the section of the rod that is less strong.
At least one blank manufacturers rates the max. line rating of the rod by the amount of weight that the blank can handle in a dead lift with the rod at a 45 degree angle. In other words at the max. line rating with the rod at a 45 degree angle the line should break before the rod does but at any angle higher than 45 degrees the rod may break before the line does. I think that all blank manufacturers should use this or a similar system and publish it so we all know what the max. line rating means.
As far as the minimum line rating is concerned, I do not think that there is any standard approach taken by blank manufacturers, or at least I have never heard of one. However, in my judgment it should be determined by the rods action (action angle). A fast action blank will handle, or cast well, a wider range of weights than a slower action rod and therefore can be used with a wider range of lines than a slower action rod. So the spread between the max. line rating on a rod and the min. line rating should be a function of the rods action. In other words the max. line rating should be a function of the dead load capacity of the rod at a 45 degree angle and the min. line rating by the rods action angle.
A side note to this is, while a fast action angle rod will handle a wider range of weights and lines, the max. line rating actually drops with a higher action angle. This is due to the fact that the higher the action angle the more stress and strain ( force and deformation) there will be of the rod toward the tip portion of the rod.

Breaking 10# line is fairly easy depending on how you set the hook , a whip set will easliy do the job. I believe the line rating is given as an indication of what load the blank will endure before failure given the load applied is 90 dergees to the rod butt.

Loads applied in a "High Sticking" fashion isolate the upper portion of the blank and will stress only that specific forshortened area, often requiring far less than the indicated load to induce failure.

Monofiliment unlike flourocarbon and and no-stretch braided or fused wonderlines do not absorb water which weakens regular monfiliment; that can absorb on as much as 8% water. This addition absorbed water may weaken the line up to one third its dry break strength. Dry 10# rated line breaks at approx a 15# load.... allowed to soften with water intake it soon breaks at appprox. 10#. So in effect the first few casts or minutes you are fishing the monofiliment line you think is within the mfg's suggested rating for a given blank when actually it exceeds the MFG's recomendation.

If you mean by 90 degrees that the butt of the rod is parallel to the ground or water and the load is directly below the tip of the rod then no the rod should take a load that is significantly higher than the maximum line rating at that angle. Consistent with your method of establishing the angle, which is probably clearer, the angle that I was referring to above would be 135 degrees.
You are correct that how rapidly the load is applied to either the line or the rod can have a significant effect but I was referring to a dead load or the load being applied at a rate that is essentially zero.