This is a linguistic approach founded by Anna Wierzbicka in the 1970s and carried on by her and her followers, mainly in Australia. The central idea is that there are a small number of concepts (about 70 -- 63 the last time I counted) and sentence types which are realized in simple forms in all languages and which, taken together in a given language, allow one to define all the words in that language in that language. Both the concepts and the sentence types have been arrived at empirically, cutting items out of an original intuitive list as ways to define them were found, adding to the list when as yet unsolved problems arose. The word list and sentence type list might then be taken as an empirical minimum for language (though this is not the point of NSM).
For constructing a language, however, this is probably not the best guideline (assuming you want to start with semantic primes or even just the smallest possible vocabulary) . For one thing, it is designed to be used in defining other terms, not in conversation or narrative exposition, so, while it does contain soome words you would need immediately (for I and you, for example), it lacks others (day, for example, or path).
For another thing, the definitions NSM provides are not (or rarely are) simple isosemic phrases of the cat = domestic felid sort. They tend rather to require an imaginative journey. Think of a situation, specified in appropriate detail, and then the word to be defined will be the appropriate thing to say: a broke b is appropriate to say when 1) a did something to b, 2) because of this something happened to b at the same time, 3) it happened in one moment, and 4) because of this afterwords b was not one thing any more. While this looks about right, it is not clear that it can be collapsed into a replacive definition and so that it could be use for the most common sort of introduction of new terms into a conlang. It is also not clear that this process will really work in more complex cases; the imagined situation may call up for the native speaker some other notion than the one sought -- or may not even apply to his experiences: the definition of green, for example, requires imagining a field of grass or other green plant, which may not be in some people's experience at all.
For all that, the theory is a viable one in linguistics, often ably attacked and often ably defended (and occasionally not so much of either). For more detailed information about the genral theory and its detailed applications -- and its controversies -- see the bibliography at