These terms are used mainly in global marketing studies, and have more to do with the weight of explicit contracts versus informal deals than with Linguistics.
Instead of analyzing languages directly, it studies communication as a whole, especially the number of things that aren't being said. It's not about grammar features, the level of usual formality, or the number of words for certain things, but the entire context surrounding a conversation and agreement, like all the cues and "rituals" people are expected to follow and assume from context.
A common example of low-context culture is the German one, where people are usually expected to be relatively "blunt" and say exactly what they mean, especially in business situations, and also be specific about all kinds of contracts and agreements. You don't need to guess much to know what a German wants from you.
On the other hand, you have high-context cultures like Brazil and Japan, where people avoid saying negative things directly and expect you to assume a great deal of things from context and get vague cues shared by their broader culture. Your subjective human relationship with your potential business partner may help you more than saying everything directly and having the most rational and detailed contracts.
A simple practical example is that when Brazilian colleagues tell you to "come over for dinner" or that "you ought to hang out some time", they might likely be just being polite and end up never making real plans with you. The outgoing Brazilian culture in general makes people say things like that just to avoid conflict and not to be seen as antisocial. If a German tells you things like that, though, he likely is serious about it and sincerely wants to have your company.
As you've said, these generalizations aren't scientific rules. Germans aren't robots and have all the same feelings as the Japanese and Brazilians. Also, culture X may be seen as higher or lower context depending on your own point of view. Brazil itself is a huge country that has different regions with their own societal norms and different "context heights". The same can be said about states within regions, specific cities and even neighborhoods within cities.
Generalizations, though, help you classify people into groups and find out what is the best strategy to target the majority of your potential clients and partners. In an ideal world, everybody would be seen as individuals, but generalizations are needed when you need quick answers and guidelines to cover segments of millions of people, especially in international trade.