What are the rules to be aware of on a road with a sign that indicates rocks might fall?

I have to add another very important point that is not listed so far: When you see this sign you should also avoid any unnecessary stops to decrease the chances to bet hit by rocks. This is in particular the case when you see this sign on hiking paths in the mountains. The sign is not only used on roads but also paths. It's not really a law though, but you should really follow this recommendation.

Here is a good example with text in English, German and French:

This signal is just a warning sign. It's information about a possible danger. You're not supposed to do anything in particular as rule. You should assume a defensive position against this event though. Whatever that means it's up to you. Locals may know about it, but you, that come from a flat land, wouldn't even suspect. There are many of these signs, that I learned in driving school, and I never saw in real life. Not all dangers are everywhere. Sometimes, when travelling one pops.

You might think it's very useless but take this example:

Imagine I aproach you and I slap you by surprise in the face. What would your reaction be? You would be completly surprised - you could run away afraid or you could even react in surprise and do the same. But I did slap you. Or maybe I just caught a mutant bug in your face that was about to kill you. You don't know!

Now, imagine someone warns you I can slap and I approach you with the same intention? what would you do? you would be prepared and could react properly!

It's the same here. You will have a more defensive attitude towards falling rocks or rocks on the road. You should assume both situations are possible. If at night, with wind or rain you will probably want to drive slower or you might even drive at the same speed if confident enough, but you will be aware of the rocks. If some fall or you hit one with your car you know what happened and will probably react in a more appropriate way. If caught by surprise you could react in unexpected ways and cause a larger accident by driving off road or against another car.

To conclude: this kind of information is very important to make you aware of possible dangers that otherwise you wouldn't know of. You should than adapt your behaviour accordingly to the risk, considering external factors as well like wind, rain, visibility and traffic conditions, but it's up to you to decide.

If you're puzzled with that sign you should look at this one, it's my favorite:

This is also a danger sign, and basically means "various dangers". You should basically prepare... anything can happen! :)

Rocks normally fall onto a road in two situations:

1. A freeze-thaw or heat/cool cycle has forced the rock out of place, causing it to fall.
2. Rain or flowing water has washed away dirt supporting the rock.

Because of this, most rockfalls occur during the early morning or during/just after rainstorms, particularly during the cooler months. If you're driving during a sunny summer afternoon, there's no real risk. On the other hand, during a rainy fall morning, you should slow down and keep an eye out for rocks lying in the road (I once encountered a half-ton boulder under these conditions). In either case, the odds of being struck by a falling rock are very low.

The German road code just specifies it as a warning sign. Source (the sign is called "Steinschlag")

That means there are no specific rules attached to this sign, but in the interest of their own safety, people should pay extra attention. The general road code already specifies that people have to drive carefully, the signs in that list are just reminders, drawing special attention to road conditions.

Specifically, Steinschlag is not listed in Anlage 1, StVO §40 which further specifies some warning signs, nor Anlage 2 to 4, where signs having an effect on road rules are listed.

I can find no indication that this is different in Spain, but I'm also not Spanish. Not all traffic signs in the EU mean the same thing when it comes to road rules.

In a nutshell: Yes, it's about rocks lying on the road and no, you might not always see them, especially on mountain roads with many bends. So it's a warning to adjust your speed (i.e. drive more slowly) and be generally alert in places where the risk is higher. As someone who has a lot of experience driving in mountain areas, I can tell you that it is useful.

The Vienna convention on road signs and signals describes the sign thusly:

11. Falling rocks

Warning of a section of road on which there is danger from falling rocks and the consequent presence of rocks on the carriageway shall be given […]

Also, to clarify: It's not mainly about huge rocks blocking the road and stopping your car but simply stones that are big enough to cause some damage or prompt you to make a dangerous manoeuvre if you see them too late.

Incidentally, because there seems to be a lot of confusion about this in the comments and some of the answers, it's easy to realise that the sign is mainly about rocks lying on the ground. Any falling rock will represent a danger for a few seconds and then lie there for hours if not days, and many more motorists will be exposed to it lying on the road rather than falling.

If there were so many rocks falling that spending a few extra minutes in the area would matter, the road would be extremely unsafe and literally covered in stones to the point that is is not usable. As @Mark aptly put it in his answer, “the odds of being struck by a falling rock are very low”. Speeding up to reduce that risk is a very bad idea, you should slow down.